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Using a power series to show $\log(2) = \sum_{k = 1}^{\infty} \frac{1}{k \cdot 2^{k}}$

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#sequences-and-series #power-series #taylor-expansion
2.7k
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Finding the Maclaurin series of $e^{\sin x}$ by comparing coefficients

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#calculus #proof-verification #power-series #taylor-expansion
94
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Why is the inequality $\sum_{n=1}^{\infty} \frac{1}{n^2} \leq 1 + \int_1^{\infty} \frac{1}{x^2}$ true?

Published on
#integration #sequences-and-series #inequality #summation #power-series
71
Views

Magic relation for harmonic numbers

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#sequences-and-series #combinatorics #power-series
68
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Do you recognize this infinite series? $\sum_{n=0}^\infty \frac 1{(1+an)^c} \frac{b^n}{n!} $

Published on
#calculus #power-series #special-functions
202
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Calculate $\sum\limits_{n=0}^{\infty} \frac{x^{3n}}{(3n)!}$

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#power-series #taylor-expansion
257
Views

Radius of convergence for $\ln(a+x)$

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#convergence-divergence #logarithms #power-series #taylor-expansion
123
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Interpolation with $p$-adic formal power series in $\mathbb Z_p[[x]]$

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#number-theory #power-series #p-adic-number-theory
104
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Radius of convergence of $\sum_0^{\infty} n!x^{n^2}$

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#real-analysis #sequences-and-series #power-series
456
Views

Using the Cauchy-Hadamard Theorem to find a radius of convergence

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#sequences-and-series #convergence-divergence #power-series #taylor-expansion
174
Views

Using Maple 2018 to find coefficients in a power series

Published on
#power-series #exponential-function #maple
468
Views

Why does $\sum_{n\geq0}(1-x)^n=\frac1x$ have such a poor radius of convergence?

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#sequences-and-series #convergence-divergence #power-series #taylor-expansion
236
Views

Write ... as a power series

Published on
#complex-analysis #power-series
280
Views

Radius of Convergence for two power series is equal.

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#complex-analysis #analysis #power-series
36
Views

Interchange of a sum and integral

Published on
#calculus #power-series

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