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Using the Cauchy root test

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#calculus #sequences-and-series #limits #convergence-divergence #power-series
281
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Complex power series: radius of convergence and derivative

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#convergence-divergence #power-series
67
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For which $x\in \mathbb{R},$ the series $\sum_{n=1}^\infty\frac{\cos^{2n}x} n$ is differentiable?

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#derivatives #summation #power-series
105
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Radius of convergence of $\,x^2\big(1+\sum_{n=1}^{\infty}\frac{(-1)^n}{(2n)!}2^{2n-1}x^{2n}\big)$

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#calculus #sequences-and-series #complex-analysis #convergence-divergence #power-series
67
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summation notation rules

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#sequences-and-series #summation #power-series
234
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How to determine the fourth coefficient in the power series expansion of $(1 + \ln(1-x))^{-1}$?

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#power-series
155
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A Question concerning the definition of Analytic functions

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#analysis #power-series #taylor-expansion #definition #analyticity
354
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Why are all analytic functions equivalent to their Taylor series?

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#real-analysis #analysis #power-series #taylor-expansion #analyticity
2.1k
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Proving $\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{2n-1}x^{2n-1}$ is differentiable

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#calculus #real-analysis #derivatives #power-series #taylor-expansion
1.7k
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Using a Taylor polynomial to calculate the error in using $x$ as an approximation for $\sin{x}$

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#calculus #power-series #taylor-expansion
220
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Finding the degree so that a Taylor polynomial yields an approximation within a specified accuracy.

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#calculus #numerical-methods #power-series
66
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Power series and computation

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#calculus #sequences-and-series #power-series
180
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Exponential convergence of Taylor series.

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#real-analysis #sequences-and-series #convergence-divergence #power-series #taylor-expansion
157
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How to solve this second-order differential equation?

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#ordinary-differential-equations #power-series #boundary-value-problem
89
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Evaluate $\lim_{x\to 1}\sum_{1}^ \infty \frac{x^n}{n(n+1)}$

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#real-analysis #sequences-and-series #power-series

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