Question

If $f_n\le g_n \le h_n$ on $\Bbb R$ and $\sum f_n$ and $\sum h_n$ converges, then $\sum g_n$ converges.

score 58 · Answer 1 · 2026-04-15 09:06:36

58

Views

If $f_n\le g_n \le h_n$ on $\Bbb R$ and $\sum f_n$ and $\sum h_n$ converges, then $\sum g_n$ converges.

Published on 15 Apr 2026 - 9:06

score 198 · Answer 2 · 2026-04-16 02:28:45

198

Views

A sequence $x_{n+1} = 3x_n + \sqrt{8x^2_n + 2}$ and find $x_{2020}$

Published on 16 Apr 2026 - 2:28

score 397 · Answer 3 · 2026-04-13 23:20:35

397

Views

Uniform convergence of sequence of functions on unbounded intervals

Published on 13 Apr 2026 - 23:20

score 90 · Answer 4 · 2026-04-15 19:45:24

90

Views

If $f_n$ continuous functions then uniform convergence of $\sum_{n=1}^{\infty}f_n$ implies continuity of limit function

Published on 15 Apr 2026 - 19:45

score 108 · Answer 5 · 2026-04-16 02:11:45

108

Views

How do you prove that $\frac{\sin x}{n \sin (\frac{x}{n})}$ converges uniformly?

Published on 16 Apr 2026 - 2:11

score 822 · Answer 6 · 2026-04-16 04:52:57

822

Views

Convergence of $f_n(x)=\frac{x}{1+nx^2}$ and its derivative $f'_n(x)=\frac{1-nx^2}{(1+nx^2)^2}$ on $\mathbb{R}$

Published on 16 Apr 2026 - 4:52

score 40 · Answer 7 · 2026-04-15 21:22:57

40

Views

Constructing a subsequence for {cos(nr)}

Published on 15 Apr 2026 - 21:22

score 705 · Answer 8 · 2026-04-09 07:23:02

705

Views

How to express a formula that iterates over itself n number of times?

Published on 09 Apr 2026 - 7:23

score 221 · Answer 9 · 2026-02-26 09:23:19

221

Views

Taylor series of $\ln(x)$ not uniformly convergent

Published on 26 Feb 2026 - 9:23

score 339 · Answer 10 · 2026-04-16 06:11:23

339

Views

Prove that $f_n$ converges uniformly on $[0,1]$ iff $\phi(1) = 0$

Published on 16 Apr 2026 - 6:11

score 679 · Answer 11 · 2026-04-14 07:37:59

679

Views

Pointwise convergence of sequence of functions on $[0,1]$

Published on 14 Apr 2026 - 7:37

score 221 · Answer 12 · 2026-04-15 12:44:37

221

Views

Uniform convergence of derivative of sequence of functions

Published on 15 Apr 2026 - 12:44

score 208 · Answer 13 · 2026-04-15 11:20:42

208

Views

Please prove that $n\cos n^2 x$ doesn't converge as $n\to\infty$ for any $x\in\mathbb{R}$.

Published on 15 Apr 2026 - 11:20

score 390 · Answer 14 · 2026-04-11 22:10:51

390

Views

How to give a rigorous proof to the divergence of $\sin nx$

Published on 11 Apr 2026 - 22:10

score 41 · Answer 15 · 2026-02-25 20:21:44

41

Views

Uniform convergence of $f_n(x)= nx/(n^2x^2+1)$

Published on 25 Feb 2026 - 20:21

List Question

If $f_n\le g_n \le h_n$ on $\Bbb R$ and $\sum f_n$ and $\sum h_n$ converges, then $\sum g_n$ converges.

A sequence $x_{n+1} = 3x_n + \sqrt{8x^2_n + 2}$ and find $x_{2020}$

Uniform convergence of sequence of functions on unbounded intervals

If $f_n$ continuous functions then uniform convergence of $\sum_{n=1}^{\infty}f_n$ implies continuity of limit function

How do you prove that $\frac{\sin x}{n \sin (\frac{x}{n})}$ converges uniformly?

Convergence of $f_n(x)=\frac{x}{1+nx^2}$ and its derivative $f'_n(x)=\frac{1-nx^2}{(1+nx^2)^2}$ on $\mathbb{R}$

Constructing a subsequence for {cos(nr)}

How to express a formula that iterates over itself n number of times?

Taylor series of $\ln(x)$ not uniformly convergent

Prove that $f_n$ converges uniformly on $[0,1]$ iff $\phi(1) = 0$

Pointwise convergence of sequence of functions on $[0,1]$

Uniform convergence of derivative of sequence of functions

Please prove that $n\cos n^2 x$ doesn't converge as $n\to\infty$ for any $x\in\mathbb{R}$.

How to give a rigorous proof to the divergence of $\sin nx$

Uniform convergence of $f_n(x)= nx/(n^2x^2+1)$

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