Question

Assume that the double sequence $(a_{m,n})_{m,n}$ converges to $0$. Then is the set $\left \{ a_{m,n}:m,n\in\mathbb{N} \right \}$ bounded?

score 108 · Answer 1 · 2026-04-15 11:14:01

108

Views

Assume that the double sequence $(a_{m,n})_{m,n}$ converges to $0$. Then is the set $\left \{ a_{m,n}:m,n\in\mathbb{N} \right \}$ bounded?

Published on 15 Apr 2026 - 11:14

score 257 · Answer 2 · 2026-04-16 11:31:06

257

Views

How can we show that $ (a_n), (b_n), (c_n) $ are convergent and have the same limit?

Published on 16 Apr 2026 - 11:31

score 131 · Answer 3 · 2026-05-10 15:29:05

131

Views

Why do Fourier transforms or Characteristic Functions converge when Laplace xforms or Moment-Generating Functions don't?

Published on 10 May 2026 - 15:29

score 117 · Answer 4 · 2026-04-17 02:36:46

117

Views

On uniform convergence of $f_n(x) = (2^n +|x|^n)^{1/n}$ for $x\in \mathbb{R}$

Published on 17 Apr 2026 - 2:36

score 86 · Answer 5 · 2026-04-15 18:35:28

86

Views

show that $\sum_{k=1}^{\infty}{\left ( \frac{1}{2} + \frac{1}{k}\right )^k}$ converges

Published on 15 Apr 2026 - 18:35

score 454 · Answer 6 · 2026-04-11 16:03:12

454

Views

Continuous function times a bounded function

Published on 11 Apr 2026 - 16:03

score 38 · Answer 7 · 2026-03-25 17:18:49

38

Views

Correctness of convergence proof

Published on 25 Mar 2026 - 17:18

score 5k · Answer 8 · 2026-05-10 11:19:29

5k

Views

Motivation for Mirror-Descent

Published on 10 May 2026 - 11:19

score 233 · Answer 9 · 2026-05-10 19:17:32

233

Views

determine whether $\int_0^\infty e^{-ax^2}dx$ converges or diverges

Published on 10 May 2026 - 19:17

score 627 · Answer 10 · 2026-05-10 18:28:00

627

Views

Determine the whether the sequence $a_{n+1} = 3 - \frac{1}{a_n} \text{ for n > 1}$ is convergent or divergent.

Published on 10 May 2026 - 18:28

score 1.3k · Answer 11 · 2026-05-10 13:48:55

1.3k

Views

Sequence of holomorphic functions converges to a holomorphic function (more details in post)

Published on 10 May 2026 - 13:48

score 267 · Answer 12 · 2026-04-12 12:23:24

267

Views

How to study the strong and weak convergence of this sequence of functions?

Published on 12 Apr 2026 - 12:23

score 241 · Answer 13 · 2026-04-14 14:02:32

241

Views

Convergence of $\sum_{n=1}^\infty \frac{\sqrt[n]{n} - 1}{n}$

Published on 14 Apr 2026 - 14:02

score 68 · Answer 14 · 2026-04-15 04:42:15

68

Views

Convergent series, by comparing ratios ($\frac{x_{n+1}}{x_n} \le \frac{y_{n+1}}{y_n}$)

Published on 15 Apr 2026 - 4:42

score 230 · Answer 15 · 2026-05-07 19:12:44

230

Views

What is the sum of reciprocal of product of $n$ primes?

Published on 07 May 2026 - 19:12

List Question

Assume that the double sequence $(a_{m,n})_{m,n}$ converges to $0$. Then is the set $\left \{ a_{m,n}:m,n\in\mathbb{N} \right \}$ bounded?

How can we show that $ (a_n), (b_n), (c_n) $ are convergent and have the same limit?

Why do Fourier transforms or Characteristic Functions converge when Laplace xforms or Moment-Generating Functions don't?

On uniform convergence of $f_n(x) = (2^n +|x|^n)^{1/n}$ for $x\in \mathbb{R}$

show that $\sum_{k=1}^{\infty}{\left ( \frac{1}{2} + \frac{1}{k}\right )^k}$ converges

Continuous function times a bounded function

Correctness of convergence proof

Motivation for Mirror-Descent

determine whether $\int_0^\infty e^{-ax^2}dx$ converges or diverges

Determine the whether the sequence $a_{n+1} = 3 - \frac{1}{a_n} \text{ for n > 1}$ is convergent or divergent.

Sequence of holomorphic functions converges to a holomorphic function (more details in post)

How to study the strong and weak convergence of this sequence of functions?

Convergence of $\sum_{n=1}^\infty \frac{\sqrt[n]{n} - 1}{n}$

Convergent series, by comparing ratios ($\frac{x_{n+1}}{x_n} \le \frac{y_{n+1}}{y_n}$)

What is the sum of reciprocal of product of $n$ primes?

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