Index stringlengths 1 5 | Challenge stringlengths 41 1.55k | Answer in Latex stringclasses 122
values | Answer in Sympy stringlengths 1 774 | Variation stringclasses 31
values | Source stringclasses 61
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|---|---|---|---|---|---|
201 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = e^{ \left(649916793\right) \sin(x)} $, where A and B are symbolic constants. | x**5*(649916793 - 10*649916793**3 + 649916793**5)/120 + x**4*(-4*649916793**2 + 649916793**4)/24 + x**3*(-649916793 + 649916793**3)/6 + x**2*649916793**2/2 + x*649916793 + 1 | Numeric-One-9 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | |
202 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = e^{ \left(9135588304\right) \sin(x)} $, where A and B are symbolic constants. | x**5*(9135588304 - 10*9135588304**3 + 9135588304**5)/120 + x**4*(-4*9135588304**2 + 9135588304**4)/24 + x**3*(-9135588304 + 9135588304**3)/6 + x**2*9135588304**2/2 + x*9135588304 + 1 | Numeric-One-10 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | |
203 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(9\right) e^{ \left(6\right) \sin(x)} $, where A and B are symbolic constants. | x**5*(6 - 10*6**3 + 6**5)*9/120 + x**4*(-4*6**2 + 6**4)*9/24 + x**3*(-6 + 6**3)*9/6 + x**2*6**2*9/2 + x*6*9 + 9 | Numeric-All-1 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | |
204 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(98\right) e^{ \left(55\right) \sin(x)} $, where A and B are symbolic constants. | x**5*(55 - 10*55**3 + 55**5)*98/120 + x**4*(-4*55**2 + 55**4)*98/24 + x**3*(-55 + 55**3)*98/6 + x**2*55**2*98/2 + x*55*98 + 98 | Numeric-All-2 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | |
205 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(286\right) e^{ \left(426\right) \sin(x)} $, where A and B are symbolic constants. | x**5*(426 - 10*426**3 + 426**5)*286/120 + x**4*(-4*426**2 + 426**4)*286/24 + x**3*(-426 + 426**3)*286/6 + x**2*426**2*286/2 + x*426*286 + 286 | Numeric-All-3 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | |
206 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(6613\right) e^{ \left(3668\right) \sin(x)} $, where A and B are symbolic constants. | x**5*(3668 - 10*3668**3 + 3668**5)*6613/120 + x**4*(-4*3668**2 + 3668**4)*6613/24 + x**3*(-3668 + 3668**3)*6613/6 + x**2*3668**2*6613/2 + x*3668*6613 + 6613 | Numeric-All-4 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | |
207 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(54737\right) e^{ \left(79738\right) \sin(x)} $, where A and B are symbolic constants. | x**5*(79738 - 10*79738**3 + 79738**5)*54737/120 + x**4*(-4*79738**2 + 79738**4)*54737/24 + x**3*(-79738 + 79738**3)*54737/6 + x**2*79738**2*54737/2 + x*79738*54737 + 54737 | Numeric-All-5 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | |
208 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(714540\right) e^{ \left(928533\right) \sin(x)} $, where A and B are symbolic constants. | x**5*(928533 - 10*928533**3 + 928533**5)*714540/120 + x**4*(-4*928533**2 + 928533**4)*714540/24 + x**3*(-928533 + 928533**3)*714540/6 + x**2*928533**2*714540/2 + x*928533*714540 + 714540 | Numeric-All-6 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | |
209 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(5068281\right) e^{ \left(3537545\right) \sin(x)} $, where A and B are symbolic constants. | x**5*(3537545 - 10*3537545**3 + 3537545**5)*5068281/120 + x**4*(-4*3537545**2 + 3537545**4)*5068281/24 + x**3*(-3537545 + 3537545**3)*5068281/6 + x**2*3537545**2*5068281/2 + x*3537545*5068281 + 5068281 | Numeric-All-7 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | |
210 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(32593878\right) e^{ \left(20771359\right) \sin(x)} $, where A and B are symbolic constants. | x**5*(20771359 - 10*20771359**3 + 20771359**5)*32593878/120 + x**4*(-4*20771359**2 + 20771359**4)*32593878/24 + x**3*(-20771359 + 20771359**3)*32593878/6 + x**2*20771359**2*32593878/2 + x*20771359*32593878 + 32593878 | Numeric-All-8 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | |
211 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(546801591\right) e^{ \left(852933933\right) \sin(x)} $, where A and B are symbolic constants. | x**5*(852933933 - 10*852933933**3 + 852933933**5)*546801591/120 + x**4*(-4*852933933**2 + 852933933**4)*546801591/24 + x**3*(-852933933 + 852933933**3)*546801591/6 + x**2*852933933**2*546801591/2 + x*852933933*546801591 + 546801591 | Numeric-All-9 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | |
212 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(6069995524\right) e^{ \left(8637358860\right) \sin(x)} $, where A and B are symbolic constants. | x**5*(8637358860 - 10*8637358860**3 + 8637358860**5)*6069995524/120 + x**4*(-4*8637358860**2 + 8637358860**4)*6069995524/24 + x**3*(-8637358860 + 8637358860**3)*6069995524/6 + x**2*8637358860**2*6069995524/2 + x*8637358860*6069995524 + 6069995524 | Numeric-All-10 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | |
213 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = e^{B \sin(x)} $, where A and B are symbolic constants. | B**2*x**2/2 + B*x + x**5*(B**5 - 10*B**3 + B)/120 + x**4*(B**4 - 4*B**2)/24 + x**3*(B**3 - B)/6 + 1 | Symbolic-1 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | |
214 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = A e^{ \sin(x)} $, where A and B are symbolic constants. | -A*x**5/15 - A*x**4/8 + A*x**2/2 + A*x + A | Symbolic-1 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | |
215 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) n \cdot ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \sinh^{2}{\left(B x \right)... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
216 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) n \cdot ( \left(\frac{\log_F\l... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
217 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \sinh^{2}{\left... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
218 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) n \cdot ( \left(\frac{F \sum_{... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
219 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) n \cdot ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( ... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
220 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) n \cdot ( \left(- \frac{2 i \l... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
221 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) n \cdot ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
222 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) n \cdot ( \left(\frac{\sinh{\l... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
223 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\ln(x) \cdo... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
224 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) n \cdot ( \left(\frac{F \sum_{... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
225 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) n \cdot ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( ... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
226 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) n \cdot ( \left(- \frac{2 i \l... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
227 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) n \cdot ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{B... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
228 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) n \cdot ( \left(\frac{\sinh{\l... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
229 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) n \cdot ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{B \sum_{N=1}^{\infty} \... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
230 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) n \cdot ( \left(\frac{\log_F\l... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
231 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) n \cdot ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( ... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
232 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) n \cdot ( \left(- \frac{2 i \l... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
233 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) n \cdot ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \frac... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
234 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) n \cdot ( \left(\frac{\sinh{\l... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
235 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) n \cdot ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \frac{i \left(e^{i B x} - e... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
236 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) n \cdot ( \left(\frac{\log_F\l... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
237 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \frac{i \left(e... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
238 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) n \cdot ( \left(\frac{F \sum_{... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
239 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) n \cdot ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\sin^{2}{\left(- B x \right... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
240 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) n \cdot ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
241 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\sin^{2}{\left(... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
242 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty ... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
243 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) n \cdot ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
244 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) n \cdot ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
245 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) n \cdot ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
246 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) n \cdot ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\lef... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
247 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\ln(x) \c... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
248 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty ... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
249 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) n \cdot ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
250 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) n \cdot ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
251 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) n \cdot ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{B... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
252 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) n \cdot ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\lef... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
253 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) n \cdot ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{B \sum_{N=1}^{\infty}... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
254 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) n \cdot ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
255 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) n \cdot ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
256 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) n \cdot ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
257 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) n \cdot ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \frac... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
258 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) n \cdot ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\lef... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
259 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) n \cdot ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \frac{i \left(e^{i B x} -... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
260 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) n \cdot ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
261 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \frac{i \left... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
262 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty ... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
263 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) n \cdot ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\sin^{2}{\left(- B x \right... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
264 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) n \cdot ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
265 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\sin^{2}{\left(- B x \right)} + \cos^... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
266 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\t... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
267 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) n \cdot ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\sin^{2}{\left... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
268 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) n \cdot ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
269 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) n \cdot ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \sinh^{2}{\left(B x \right)... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
270 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) n \cdot ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
271 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \sinh^{2}{\left(B x \right)} + \cos... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
272 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\s... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
273 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) n \cdot ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \sinh^{2}{\l... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
274 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) n \cdot ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
275 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) n \cdot ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{B \sum_{N=1}^{\infty} \... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
276 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) n \cdot ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
277 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) n \cdot ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{B \sum_{N=1}^{\infty}... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
278 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) n \cdot ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
279 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) n \cdot ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{B \sum_{... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
280 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) n \cdot ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
281 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) n \cdot ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \frac{i \left(e^{i B x} - e... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
282 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) n \cdot ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
283 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) n \cdot ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \frac{i \left(e^{i B x} -... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
284 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) n \cdot ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
285 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \frac{i \left(e^{i B x} - e^{- i B ... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
286 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \frac{... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
287 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) n \cdot ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\sin^{2}{\left(... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
288 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) n \cdot ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty ... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
289 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) n \cdot ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\sin^{2}{\left(- B x \right)} + \cos^... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
290 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) n \cdot ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\t... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
291 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) n \cdot ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\s... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
292 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) n \cdot ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
293 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) n \cdot ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \sinh^{2}{\left... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
294 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) n \cdot ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right)... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
295 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) n \cdot ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \sinh^{2}{\left(B x \right)} + \cos... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
296 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) n \cdot ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\s... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
297 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) n \cdot ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- ... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
298 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) n \cdot ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
299 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) n \cdot ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\ln(x) \cdo... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a | |
300 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) n \cdot ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right)... | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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