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Finding closed form for this series

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#calculus #sequences-and-series #limits #analysis #power-series
1.1k
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How to evaluate $\sum\limits_{n=0}^\infty n^3x^n$, for $x\in[0,1)$.

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#calculus #summation #power-series
44
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Why $f \mid V(m) \mid U(m) = f$ for modular form $f$, where $U, V$ are $U, V$-operators?

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#power-series #fourier-series #modular-forms
305
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Recurrent series from Euler

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#calculus #sequences-and-series #power-series #taylor-expansion
34
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Asymptotic properties of a power series

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#sequences-and-series #convergence-divergence #power-series
42
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Determine if the series is abs. convergent, conditionally convergent, or divergent

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#calculus #sequences-and-series #power-series
76
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Sum of x raised to odd powers till infinity where x is less than 0

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#summation #power-series
28
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Power series of $\frac{1}{(x-1)(x-2)}$ at $x=0$

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#analysis #power-series
182
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Must a complex power series be unbounded within its radius of convergence?

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#complex-analysis #power-series
80
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Proof of $f(x) = \sum_{k=0}^\infty a_kx^k$ with $a_0 := a_1 := 1$ and $a_{n+2} := a_n+a_{n+1}$

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#analysis #power-series #alternative-proof #recursion #fibonacci-numbers
49
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Give an example of a function that converges to its Taylor series for $x\geq 0$ but not for $x<0$.

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#real-analysis #sequences-and-series #power-series #taylor-expansion #uniform-convergence
59
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Writing $e^{\frac{-1}{\epsilon}}$ as a sum $\sum_{n>0}a_n.\epsilon^n$

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#real-analysis #power-series
62
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Radius of convergence of a particular power series

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#real-analysis #sequences-and-series #limits #convergence-divergence #power-series
115
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Find Taylor Series of $(3x^2 + 2x -7)e^{5x}$

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#sequences-and-series #power-series #taylor-expansion
43
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Calculate $\sum^\infty _{k=1} \frac{10^{-k-1}}{k(k+1)}$ using the Taylor series of $(1-x)\ln(1-x)$

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#sequences-and-series #convergence-divergence #summation #power-series #taylor-expansion

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