Question

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

score 144 · Answer 1 · 2026-02-23 19:22:36

144

Views

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

Published on 23 Feb 2026 - 19:22

score 107 · Answer 2 · 2019-08-05 17:33:43

107

Views

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

Published on 05 Aug 2019 - 17:33

score 48 · Answer 3 · 2026-03-25 22:09:36

48

Views

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

Published on 25 Mar 2026 - 22:09

score 59 · Answer 4 · 2026-02-23 19:22:15

59

Views

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

Published on 23 Feb 2026 - 19:22

score 102 · Answer 5 · 2019-08-07 21:25:56

102

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 07 Aug 2019 - 21:25

score 31 · Answer 6 · 2026-02-23 05:15:43

31

Views

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

Published on 23 Feb 2026 - 5:15

score 67 · Answer 7 · 2019-08-09 01:56:33

67

Views

Show that following series is uniformly convergent.

Published on 09 Aug 2019 - 1:56

score 378 · Answer 8 · 2026-02-23 06:36:22

378

Views

Peano's Existence Theorem: Questions about the proof

Published on 23 Feb 2026 - 6:36

score 167 · Answer 9 · 2019-08-10 19:54:08

167

Views

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

Published on 10 Aug 2019 - 19:54

score 164 · Answer 10 · 2026-03-24 14:22:27

164

Views

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

Published on 24 Mar 2026 - 14:22

score 145 · Answer 11 · 2026-02-23 19:15:17

145

Views

Uniform convergence of exponential function

Published on 23 Feb 2026 - 19:15

score 293 · Answer 12 · 2026-03-29 18:19:57

293

Views

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

Published on 29 Mar 2026 - 18:19

score 152 · Answer 13 · 2019-08-13 12:42:27

152

Views

Isn't Abel's limit theorem trivial?

Published on 13 Aug 2019 - 12:42

score 159 · Answer 14 · 2026-03-24 16:44:53

159

Views

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

Published on 24 Mar 2026 - 16:44

score 201 · Answer 15 · 2026-03-30 02:11:29

201

Views

Uniform convergence of fourier series of step function

Published on 30 Mar 2026 - 2:11

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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