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 55 · Answer 1 · 2021-01-20 12:47:35

55

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 20 Jan 2021 - 12:47

score 195 · Answer 2 · 2021-01-23 09:49:03

195

Views

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

Published on 23 Jan 2021 - 9:49

score 395 · Answer 3 · 2021-01-24 03:49:52

395

Views

Uniform convergence of sequence of functions on unbounded intervals

Published on 24 Jan 2021 - 3:49

score 87 · Answer 4 · 2021-01-30 19:10:48

87

Views

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

Published on 30 Jan 2021 - 19:10

score 105 · Answer 5 · 2021-02-15 05:45:55

105

Views

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

Published on 15 Feb 2021 - 5:45

score 820 · Answer 6 · 2021-02-18 04:52:53

820

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 18 Feb 2021 - 4:52

score 38 · Answer 7 · 2026-02-25 18:36:55

38

Views

Constructing a subsequence for {cos(nr)}

Published on 25 Feb 2026 - 18:36

score 702 · Answer 8 · 2021-02-21 20:04:27

702

Views

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

Published on 21 Feb 2021 - 20:04

score 220 · Answer 9 · 2021-02-24 23:08:57

220

Views

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

Published on 24 Feb 2021 - 23:08

score 336 · Answer 10 · 2021-02-27 12:50:32

336

Views

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

Published on 27 Feb 2021 - 12:50

score 677 · Answer 11 · 2026-02-25 18:40:17

677

Views

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

Published on 25 Feb 2026 - 18:40

score 218 · Answer 12 · 2021-03-01 05:51:49

218

Views

Uniform convergence of derivative of sequence of functions

Published on 01 Mar 2021 - 5:51

score 205 · Answer 13 · 2021-03-02 02:49:03

205

Views

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

Published on 02 Mar 2021 - 2:49

score 387 · Answer 14 · 2021-03-06 05:31:18

387

Views

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

Published on 06 Mar 2021 - 5:31

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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