Question

If $\sum_j \frac 1 j a_j $ is summable where $\{a_k\}$ is a positive sequence, then is $\liminf a_k = 0$?

score 50 · Answer 1 · 2026-04-14 09:16:55

50

Views

If $\sum_j \frac 1 j a_j $ is summable where $\{a_k\}$ is a positive sequence, then is $\liminf a_k = 0$?

Published on 14 Apr 2026 - 9:16

score 70 · Answer 2 · 2026-04-15 20:40:03

70

Views

Why can we interchange the order of limits here?

Published on 15 Apr 2026 - 20:40

score 207 · Answer 3 · 2026-04-15 17:09:37

207

Views

Find the domain of $x$ for the convergence of the series $\sum_{n=1}^{\infty} \left(\frac{\ln(n)}{n}\right)^{x}$

Published on 15 Apr 2026 - 17:09

score 403 · Answer 4 · 2026-05-10 13:28:09

403

Views

Prove that if $f$ lies in $L^{1}({\bf R}^{n})$ then $\widehat f$ is uniformly continuous on ${\bf R}^{n},$

Published on 10 May 2026 - 13:28

score 286 · Answer 5 · 2026-04-15 17:35:38

286

Views

Determine whether the series $\sum_{n=1}^{\infty}\left(\frac{n}{n+1}\right)^{n^2}$ converges

Published on 15 Apr 2026 - 17:35

score 604 · Answer 6 · 2026-04-17 02:57:48

604

Views

Find the range of $x$ for the convergence of the series $\sum_{n=1}^{\infty} \frac{1}{\left(-3\right)^{n+2}} \frac{\left(4x-12\right)^{n}}{n^{2}+1}$

Published on 17 Apr 2026 - 2:57

score 110 · Answer 7 · 2026-05-10 12:57:17

110

Views

Find $\sum_{n=1}^{\infty} n\left(2n-1\right)x^{2n}$

Published on 10 May 2026 - 12:57

score 68 · Answer 8 · 2026-04-14 23:58:25

68

Views

Series Convergence of $ \sum_{n=1}^{\infty}\frac{1}{n}\int_{0}^{1}f(x)e^{-nx}dx$

Published on 14 Apr 2026 - 23:58

score 59 · Answer 9 · 2026-04-29 12:48:35

59

Views

Does one-sided derivative of real power series at edge of domain of convergence

Published on 29 Apr 2026 - 12:48

score 158 · Answer 10 · 2026-04-29 12:42:42

158

Views

Uniform Convergence of the Sequence of the function: $f_n(x) = \frac{1}{1+nx^2}, x\in \mathbb{R}$

Published on 29 Apr 2026 - 12:42

score 57 · Answer 11 · 2026-05-10 14:07:47

57

Views

Bounds on asymptotics of function series in terms of asymptotics of summands

Published on 10 May 2026 - 14:07

score 259 · Answer 12 · 2026-04-29 12:28:50

259

Views

Convergence of ratio of two sums of uniform random variables

Published on 29 Apr 2026 - 12:28

score 149 · Answer 13 · 2026-04-14 02:49:09

149

Views

convergence of $ \sum_{k=1}^{\infty}{ \frac{1}{\sqrt{k(k+1)}} } $

Published on 14 Apr 2026 - 2:49

score 220 · Answer 14 · 2026-05-10 15:09:07

220

Views

help with sum of infinite series, stuck in problem

Published on 10 May 2026 - 15:09

score 136 · Answer 15 · 2026-05-06 10:03:54

136

Views

$\frac1n \sum_{i=1}^n W_i(T_i)\to 0$ a.s. for $n\to\infty$

Published on 06 May 2026 - 10:03

List Question

If $\sum_j \frac 1 j a_j $ is summable where $\{a_k\}$ is a positive sequence, then is $\liminf a_k = 0$?

Why can we interchange the order of limits here?

Find the domain of $x$ for the convergence of the series $\sum_{n=1}^{\infty} \left(\frac{\ln(n)}{n}\right)^{x}$

Prove that if $f$ lies in $L^{1}({\bf R}^{n})$ then $\widehat f$ is uniformly continuous on ${\bf R}^{n},$

Determine whether the series $\sum_{n=1}^{\infty}\left(\frac{n}{n+1}\right)^{n^2}$ converges

Find the range of $x$ for the convergence of the series $\sum_{n=1}^{\infty} \frac{1}{\left(-3\right)^{n+2}} \frac{\left(4x-12\right)^{n}}{n^{2}+1}$

Find $\sum_{n=1}^{\infty} n\left(2n-1\right)x^{2n}$

Series Convergence of $ \sum_{n=1}^{\infty}\frac{1}{n}\int_{0}^{1}f(x)e^{-nx}dx$

Does one-sided derivative of real power series at edge of domain of convergence

Uniform Convergence of the Sequence of the function: $f_n(x) = \frac{1}{1+nx^2}, x\in \mathbb{R}$

Bounds on asymptotics of function series in terms of asymptotics of summands

Convergence of ratio of two sums of uniform random variables

convergence of $ \sum_{k=1}^{\infty}{ \frac{1}{\sqrt{k(k+1)}} } $

help with sum of infinite series, stuck in problem

$\frac1n \sum_{i=1}^n W_i(T_i)\to 0$ a.s. for $n\to\infty$

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