Question

Uniform convergence of the sum $\sum_{n=0}^\infty {(n+1)x^n}$, $|x| < 1$

score 474 · Answer 1 · 2026-04-17 14:29:37

474

Views

Uniform convergence of the sum $\sum_{n=0}^\infty {(n+1)x^n}$, $|x| < 1$

Published on 17 Apr 2026 - 14:29

score 484 · Answer 2 · 2026-04-16 13:01:58

484

Views

Proof that a uniform continuous function preserves uniform convergence of sequence of measurable functions

Published on 16 Apr 2026 - 13:01

score 113 · Answer 3 · 2026-04-17 19:43:59

113

Views

Monotonicity of sequence of functions - Dini's theorem

Published on 17 Apr 2026 - 19:43

score 74 · Answer 4 · 2026-04-16 12:03:40

74

Views

Uniform convergence of $\sum_{n=1}^{\infty} \frac{x^{n+1} + 2 \cos(x)}{(n^2+1)(x^n+1)}$

Published on 16 Apr 2026 - 12:03

score 172 · Answer 5 · 2026-04-17 08:42:36

172

Views

What an example of holomorphic function $f_n\to f$ s.t. $f$ is not holomorphic?

Published on 17 Apr 2026 - 8:42

score 186 · Answer 6 · 2026-04-15 17:55:46

186

Views

$f_n(x) = \int_{0}^1 t^{x-1} (1-t)^{n-1} dt$ does not converge uniformly to zero in $(0,\infty)$

Published on 15 Apr 2026 - 17:55

score 60 · Answer 7 · 2026-04-15 20:35:27

60

Views

condition for uniform convergence of $\sum_{n=1}^{\infty} a_n \max\{0,1-|x-2n|\}$

Published on 15 Apr 2026 - 20:35

score 361 · Answer 8 · 2026-04-10 10:36:46

361

Views

Eigenfunction expansion and boundary conditions - understanding the nuances

Published on 10 Apr 2026 - 10:36

score 125 · Answer 9 · 2026-04-17 08:31:04

125

Views

Is a continuous function necessarily the pointwise limit of a sequence of uniformly continuous functions?

Published on 17 Apr 2026 - 8:31

score 42 · Answer 10 · 2026-04-17 14:59:29

42

Views

uniform convergence of $\left(\frac{x^2}{1+x^2} \right)^n$

Published on 17 Apr 2026 - 14:59

score 78 · Answer 11 · 2026-04-17 20:02:06

78

Views

Does $f_n(x)=\sin(x)^{1/n}$ uniformly converge in $I=[\frac {\pi}{4},\frac {3\pi}{4}]$

Published on 17 Apr 2026 - 20:02

score 56 · Answer 12 · 2026-04-13 21:48:19

56

Views

Confused to determine $f_n(x)$ is uniformly convergent or not.

Published on 13 Apr 2026 - 21:48

score 75 · Answer 13 · 2026-04-14 18:22:21

75

Views

Uniform convergence of the sequence of functions

Published on 14 Apr 2026 - 18:22

score 601 · Answer 14 · 2026-04-16 20:56:54

601

Views

$f_n$ bounded functions, converges uniformly, then $\lim _{n \rightarrow \infty} (R)\int_{a}^{b} f_{n}=(R)\int_{a}^{b} f$

Published on 16 Apr 2026 - 20:56

score 94 · Answer 15 · 2026-04-15 20:25:32

94

Views

Uniform convergence and triangle inequality

Published on 15 Apr 2026 - 20:25

List Question

Uniform convergence of the sum $\sum_{n=0}^\infty {(n+1)x^n}$, $|x| < 1$

Proof that a uniform continuous function preserves uniform convergence of sequence of measurable functions

Monotonicity of sequence of functions - Dini's theorem

Uniform convergence of $\sum_{n=1}^{\infty} \frac{x^{n+1} + 2 \cos(x)}{(n^2+1)(x^n+1)}$

What an example of holomorphic function $f_n\to f$ s.t. $f$ is not holomorphic?

$f_n(x) = \int_{0}^1 t^{x-1} (1-t)^{n-1} dt$ does not converge uniformly to zero in $(0,\infty)$

condition for uniform convergence of $\sum_{n=1}^{\infty} a_n \max\{0,1-|x-2n|\}$

Eigenfunction expansion and boundary conditions - understanding the nuances

Is a continuous function necessarily the pointwise limit of a sequence of uniformly continuous functions?

uniform convergence of $\left(\frac{x^2}{1+x^2} \right)^n$

Does $f_n(x)=\sin(x)^{1/n}$ uniformly converge in $I=[\frac {\pi}{4},\frac {3\pi}{4}]$

Confused to determine $f_n(x)$ is uniformly convergent or not.

Uniform convergence of the sequence of functions

$f_n$ bounded functions, converges uniformly, then $\lim _{n \rightarrow \infty} (R)\int_{a}^{b} f_{n}=(R)\int_{a}^{b} f$

Uniform convergence and triangle inequality

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