Question

There exist infinitely many subsequences of $(f_{m})_{m \geq 1}$ which converge at every point of $E$

score 103 · Answer 1 · 2020-05-14 22:01:15

There exist infinitely many subsequences of $(f_{m})_{m \geq 1}$ which converge at every point of $E$

Published on 14 May 2020 - 22:01

score 44 · Answer 2 · 2020-05-14 22:12:49

Prove $ \lim_{x\to \infty} f^{'}_n(x)=f^{'}(x) $, being $ f_n(x)=\frac{\sqrt{(1-x^2)^{n^2+1}}}{n} , \forall{x}\in{[-1,1], \forall{n}\in{\mathbb{N}}}$

score 75 · Answer 3 · 2020-05-15 00:05:55

75

Views

Am I proving correctly that the uniform convergence of the product is the product of the limits when each sequence is uniformly bounded?

Published on 15 May 2020 - 0:05

score 48 · Answer 4 · 2020-05-15 10:50:20

48

Views

Show that the derivative of a series $\sum_{n=1}^\infty \frac{-2x}{(2+x^2)^{n+1}}$ converges uniformly

Published on 15 May 2020 - 10:50

score 49 · Answer 5 · 2020-05-15 14:39:34

49

Views

Given $f_n(x) := \cos{(x+\frac{1}{\sqrt{n}})}$. Does ${f_n(x)}_{n \geq 1}$ converge uniformly on $\mathbb R$?

Published on 15 May 2020 - 14:39

score 48 · Answer 6 · 2026-02-24 14:26:42

48

Views

Check: $\lim_{n\to \infty} f^{'}_n(x)=f^{'}(x)$

Published on 24 Feb 2026 - 14:26

score 513 · Answer 7 · 2026-02-24 14:26:15

513

Views

Uniform Convergence of $e^{-nx}$ on $[0,1]$, $[a,1]$, $(0,1]$

Published on 24 Feb 2026 - 14:26

score 724 · Answer 8 · 2020-05-16 14:24:24

724

Views

Show that series converges uniformly?

Published on 16 May 2020 - 14:24

score 168 · Answer 9 · 2020-05-17 16:35:56

168

Views

$\sum_{n=1}^{\infty} f_n$ is converges uniformly if $\sum_{n=1}^{\infty} a_n$ converges and $|f_n(x)|<a_n$

Published on 17 May 2020 - 16:35

score 85 · Answer 10 · 2020-05-17 17:33:39

85

Views

Prove that this complex series converges uniformly

Published on 17 May 2020 - 17:33

score 31 · Answer 11 · 2020-05-17 19:40:04

31

Views

Convergence of sum of function values when the function is integrable

Published on 17 May 2020 - 19:40

score 81 · Answer 12 · 2020-05-17 20:11:54

81

Views

prove or disprove $\sum_{n=1}^\infty \frac{(-1)^{n+1}}{x^2+2n- \sin nx}$ converge uniformly in $\mathbb{R}$

Published on 17 May 2020 - 20:11

score 63 · Answer 13 · 2020-05-18 21:13:03

63

Views

Showing that $\frac{z^n}{n^2+z^n}$ converges uniformly

Published on 18 May 2020 - 21:13

score 90 · Answer 14 · 2026-02-24 07:04:52

90

Views

Exercise involving pointwise and uniform convergence: why does it converge and why it does not converge?

Published on 24 Feb 2026 - 7:04

score 65 · Answer 15 · 2020-05-19 03:33:05

65

Views

Prove that $f_n(x) = \frac{x^2 + nx + 3}{n}$ converges uniformly over [1,2]

Published on 19 May 2020 - 3:33

List Question

There exist infinitely many subsequences of $(f_{m})_{m \geq 1}$ which converge at every point of $E$

Prove $ \lim_{x\to \infty} f^{'}_n(x)=f^{'}(x) $, being $ f_n(x)=\frac{\sqrt{(1-x^2)^{n^2+1}}}{n} , \forall{x}\in{[-1,1], \forall{n}\in{\mathbb{N}}}$

Am I proving correctly that the uniform convergence of the product is the product of the limits when each sequence is uniformly bounded?

Show that the derivative of a series $\sum_{n=1}^\infty \frac{-2x}{(2+x^2)^{n+1}}$ converges uniformly

Given $f_n(x) := \cos{(x+\frac{1}{\sqrt{n}})}$. Does ${f_n(x)}_{n \geq 1}$ converge uniformly on $\mathbb R$?

Check: $\lim_{n\to \infty} f^{'}_n(x)=f^{'}(x)$

Uniform Convergence of $e^{-nx}$ on $[0,1]$, $[a,1]$, $(0,1]$

Show that series converges uniformly?

$\sum_{n=1}^{\infty} f_n$ is converges uniformly if $\sum_{n=1}^{\infty} a_n$ converges and $|f_n(x)|<a_n$

Prove that this complex series converges uniformly

Convergence of sum of function values when the function is integrable

prove or disprove $\sum_{n=1}^\infty \frac{(-1)^{n+1}}{x^2+2n- \sin nx}$ converge uniformly in $\mathbb{R}$

Showing that $\frac{z^n}{n^2+z^n}$ converges uniformly

Exercise involving pointwise and uniform convergence: why does it converge and why it does not converge?

Prove that $f_n(x) = \frac{x^2 + nx + 3}{n}$ converges uniformly over [1,2]

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