List questions from convergence-divergence

Published on 25 Mar 2026 - 17:52

19

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If $i$ is recurrent then expected recurrence time is the limit of $\frac 1 {(1-s)p_{ii}(s)}$

Published on 25 Mar 2026 - 12:50

149

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$\lim_{n\rightarrow\infty}\sum_{r=0}^{n-1}\sum_{k=0}^{n-r}(-1)^k\frac{2n+3}{k!(2n+3-k)!} (1+n-r-k)^{2n+1}=0$

Published on 26 Mar 2026 - 12:15

72

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Does the following $\sin$-series converges?

Published on 14 May 2018 - 10:41

153

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Evaluate the integral $\int_0^\infty \frac{\sin(ax)}{x} \frac{\sin(bx)}{x}e^{-kx}dx$

Published on 26 Mar 2026 - 1:10

14

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Existence of threshold in function

Published on 03 Mar 2026 - 15:50

252

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Convergent series after rearrangement becomes divergent

Published on 14 May 2018 - 14:33

126

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(Non-) Convergence of $\frac{1}{n} \sum_{k=0}^{n - 1} \exp\left(2i \pi [\frac{3 + \sqrt{5}}{2}]^k\right)$ when $n \to +\infty$

Published on 30 Mar 2026 - 19:44

178

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Does $\sum_{n=1}^\infty \frac{n^{n+\frac{1}{n}}}{(n+\frac{1}{n})^n}$ converge?

Published on 14 May 2018 - 23:48

322

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Expected value of the reciprocal

Published on 27 Mar 2026 - 0:02

185

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Infinite sum of little Oh terms

Published on 15 May 2018 - 16:55

89

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Does $\lim_{n\to\infty}\left(4\sum_{i=1}^{2n}(-1)^i\sqrt{i}\right)-\sqrt{2n}-\sqrt{2n+1}$ converge?

Published on 27 Mar 2026 - 18:27

257

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Does absolute convergence imply the convergence of square of the sequence?

Published on 26 Mar 2026 - 9:42

77

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convergence criteria from real to complex domains?

Published on 16 May 2018 - 14:35

380

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If $|a_1|>1$, then the series $\sum\frac{a_1^n+\cdots+a_k^n}{n}$ diverges

Published on 17 May 2018 - 9:08

List Question

Is this Evaluation of definite Integral correct?

If $i$ is recurrent then expected recurrence time is the limit of $\frac 1 {(1-s)p_{ii}(s)}$

$\lim_{n\rightarrow\infty}\sum_{r=0}^{n-1}\sum_{k=0}^{n-r}(-1)^k\frac{2n+3}{k!(2n+3-k)!} (1+n-r-k)^{2n+1}=0$

Does the following $\sin$-series converges?

Evaluate the integral $\int_0^\infty \frac{\sin(ax)}{x} \frac{\sin(bx)}{x}e^{-kx}dx$

Existence of threshold in function

Convergent series after rearrangement becomes divergent

(Non-) Convergence of $\frac{1}{n} \sum_{k=0}^{n - 1} \exp\left(2i \pi [\frac{3 + \sqrt{5}}{2}]^k\right)$ when $n \to +\infty$

Does $\sum_{n=1}^\infty \frac{n^{n+\frac{1}{n}}}{(n+\frac{1}{n})^n}$ converge?

Expected value of the reciprocal

Infinite sum of little Oh terms

Does $\lim_{n\to\infty}\left(4\sum_{i=1}^{2n}(-1)^i\sqrt{i}\right)-\sqrt{2n}-\sqrt{2n+1}$ converge?

Does absolute convergence imply the convergence of square of the sequence?

convergence criteria from real to complex domains?

If $|a_1|>1$, then the series $\sum\frac{a_1^n+\cdots+a_k^n}{n}$ diverges

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