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What does it mean to say it "converges geometrically"

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#sequences-and-series #convergence-divergence #power-series #approximation #geometric-series
311
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Can the radius of convergence of a sum of two power series be an arbitrary number?

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#complex-analysis #convergence-divergence #power-series #analytic-functions
52
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Summing a series exactly 1

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#sequences-and-series #summation #power-series
168
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Is there a non zero power series that always converges to $0$?

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#calculus #power-series
306
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A power series with real coefficients which evaluates to $0$ for every positive real number

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#real-analysis #complex-analysis #power-series #entire-functions
713
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Analytic and circle of convergence

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#complex-analysis #convergence-divergence #power-series #analytic-functions
61
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Convergence of $\sum_{n=1}^\infty \frac{z^{n!}}{n^2}$ where $\vert z\vert = 1$?

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#sequences-and-series #complex-numbers #power-series
169
Views

Sum to infinity series: $\sum_{k=0}^{\infty}\frac{(k+1)(k+3)(-1)^k}{3^k}$

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#sequences-and-series #convergence-divergence #summation #power-series
237
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Real analytic function is uniquely determined by its derivatives at $0$

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#real-analysis #power-series
322
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Relation between two series

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#sequences-and-series #power-series #arithmetic-progressions #geometric-series #geometric-progressions
67
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Find the power series of $f(x)=\frac{x}{x+1}$ in $x_0=0$

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#sequences-and-series #power-series #cauchy-product
362
Views

Radius of convergence comparison for power series

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#real-analysis #power-series
61
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How to solve this expression: $\sum_{n=1}^\infty\frac1{(x-3)^{2n-1}}$

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#integration #sequences-and-series #power-series
57
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simple question on euler product of zeta function

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#number-theory #algebraic-geometry #power-series #zeta-functions
598
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Show power series converges for every $x$.

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#real-analysis #convergence-divergence #power-series #lipschitz-functions

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