Question

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

score 147 · Answer 1 · 2026-04-15 20:01:04

147

Views

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

Published on 15 Apr 2026 - 20:01

score 110 · Answer 2 · 2026-04-14 14:52:16

110

Views

Compute closed form of $\sum_{k = 1}^{\infty} \frac{k}{3^{k}}$

Published on 14 Apr 2026 - 14:52

score 50 · Answer 3 · 2026-04-10 22:10:33

50

Views

Can we approximate uniformly a function defined on a subset with smooth functions?

Published on 10 Apr 2026 - 22:10

score 62 · Answer 4 · 2026-04-14 23:32:39

62

Views

$\{g_n\}$ be uniformly bounded sequence of functions on $[0,1]$ and converges pointwise to $g$.

Published on 14 Apr 2026 - 23:32

score 105 · Answer 5 · 2026-04-11 18:09:57

105

Views

Why is $\sum_{k = 0}^{\infty}(-x^{2})^{k}$ not uniformly convergent on $(-1,1)$ but it is on $[-r,r] \subset (-1,1)$? Clarification

Published on 11 Apr 2026 - 18:09

score 32 · Answer 6 · 2026-04-09 10:04:36

32

Views

Determine if the following family, $\mathcal{F}$, of continuous functions is compact: $\{x^{n}\} \cup \{0\}$ in $[0,\frac{1}{2}]$

Published on 09 Apr 2026 - 10:04

score 69 · Answer 7 · 2026-04-15 06:07:46

69

Views

Show that following series is uniformly convergent.

Published on 15 Apr 2026 - 6:07

score 379 · Answer 8 · 2026-04-09 15:22:33

379

Views

Peano's Existence Theorem: Questions about the proof

Published on 09 Apr 2026 - 15:22

score 170 · Answer 9 · 2026-04-13 10:59:07

170

Views

Show that a certain subset of $C[0,1]$ is not closed.

Published on 13 Apr 2026 - 10:59

score 165 · Answer 10 · 2026-04-11 17:19:48

165

Views

Does $f_{n}(z) = \frac{1}{1+n^{2}|z-e^{in}|}$ converge pointwise or uniformly?

Published on 11 Apr 2026 - 17:19

score 148 · Answer 11 · 2026-04-14 18:22:10

148

Views

Uniform convergence of exponential function

Published on 14 Apr 2026 - 18:22

score 294 · Answer 12 · 2026-04-14 11:23:52

294

Views

Convergence in distribution of the digits of uniform random variables to one Uniform(0,1)

Published on 14 Apr 2026 - 11:23

score 155 · Answer 13 · 2026-04-09 16:02:55

155

Views

Isn't Abel's limit theorem trivial?

Published on 09 Apr 2026 - 16:02

score 160 · Answer 14 · 2026-04-11 14:09:19

160

Views

If a sequence of functions $\{f_n\}$ be uniformly convergent on $[a,b]$, would it be uniformly convergent of $(a,b)$?

Published on 11 Apr 2026 - 14:09

score 203 · Answer 15 · 2026-04-12 10:23:32

203

Views

Uniform convergence of fourier series of step function

Published on 12 Apr 2026 - 10:23

List Question

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

Compute closed form of $\sum_{k = 1}^{\infty} \frac{k}{3^{k}}$

Can we approximate uniformly a function defined on a subset with smooth functions?

$\{g_n\}$ be uniformly bounded sequence of functions on $[0,1]$ and converges pointwise to $g$.

Why is $\sum_{k = 0}^{\infty}(-x^{2})^{k}$ not uniformly convergent on $(-1,1)$ but it is on $[-r,r] \subset (-1,1)$? Clarification

Determine if the following family, $\mathcal{F}$, of continuous functions is compact: $\{x^{n}\} \cup \{0\}$ in $[0,\frac{1}{2}]$

Show that following series is uniformly convergent.

Peano's Existence Theorem: Questions about the proof

Show that a certain subset of $C[0,1]$ is not closed.

Does $f_{n}(z) = \frac{1}{1+n^{2}|z-e^{in}|}$ converge pointwise or uniformly?

Uniform convergence of exponential function

Convergence in distribution of the digits of uniform random variables to one Uniform(0,1)

Isn't Abel's limit theorem trivial?

If a sequence of functions $\{f_n\}$ be uniformly convergent on $[a,b]$, would it be uniformly convergent of $(a,b)$?

Uniform convergence of fourier series of step function

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