Question

Understanding a subsequence converges in the proof of completeness of $L^p$ in Stein-Shakarchi's Functional Analysis

score 161 · Answer 1 · 2026-04-09 18:00:41

161

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Understanding a subsequence converges in the proof of completeness of $L^p$ in Stein-Shakarchi's Functional Analysis

Published on 09 Apr 2026 - 18:00

score 845 · Answer 2 · 2026-04-09 00:43:39

845

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How to prove a Ramanujan-type series for Pi?

Published on 09 Apr 2026 - 0:43

score 36 · Answer 3 · 2026-04-14 02:12:13

36

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A question of convergence of a series closely related to two sequences of prime numbers

Published on 14 Apr 2026 - 2:12

score 228 · Answer 4 · 2026-04-16 07:40:25

228

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Intuition: $]0,\infty[: \{x \mapsto \arctan{(nx)}: n \in \mathbb N\}$

Published on 16 Apr 2026 - 7:40

score 247 · Answer 5 · 2026-04-13 20:30:03

247

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Why does Brent/Salamin algorithm double the digits of $\pi$ with each iteration?

Published on 13 Apr 2026 - 20:30

score 31 · Answer 6 · 2026-04-12 01:10:38

31

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Limit of expectation of stochastic process

Published on 12 Apr 2026 - 1:10

score 176 · Answer 7 · 2026-04-16 02:57:01

176

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Convergence of the sequence $x_n= \frac{1}{n+1}+\frac{1}{n+2}+\dots+\frac{1}{2n}$

Published on 16 Apr 2026 - 2:57

score 55 · Answer 8 · 2026-04-16 20:18:14

55

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Why do we have $(1+\frac{c}{n}+o(\frac{1}{n}))^n \to e^c$ as $n \to \infty?$

Published on 16 Apr 2026 - 20:18

score 1k · Answer 9 · 2026-04-13 19:47:54

1k

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Number of fixed points converges to poisson distribution?

Published on 13 Apr 2026 - 19:47

score 40 · Answer 10 · 2026-04-14 00:32:38

40

Views

Prove that $\sum_{k=0}^{\infty}{\frac{(3i)^k}{k!}}$ converges .

Published on 14 Apr 2026 - 0:32

score 237 · Answer 11 · 2026-04-16 05:43:50

237

Views

Prove the divergence of $\sum_{k=0}^{\infty}{\frac{1}{10k+1}}$

Published on 16 Apr 2026 - 5:43

score 91 · Answer 12 · 2026-04-16 14:22:05

91

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Proof that if $\sum_{n}|f_{n}(z)|$ converges, then $\prod_{n}(1+f_{n}(z))$ converges.

Published on 16 Apr 2026 - 14:22

score 68 · Answer 13 · 2026-04-15 02:48:37

68

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Prove the divergence of $\sum_{k=1}^{\infty}{\frac{k}{\sqrt[3]{k+1}}}$ (Alternative proofs)

Published on 15 Apr 2026 - 2:48

score 98 · Answer 14 · 2026-04-17 09:02:47

98

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Distance from a closed set.

Published on 17 Apr 2026 - 9:02

score 62 · Answer 15 · 2026-04-11 15:04:10

62

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Exercise on pointwise convergence

Published on 11 Apr 2026 - 15:04

List Question

Understanding a subsequence converges in the proof of completeness of $L^p$ in Stein-Shakarchi's Functional Analysis

How to prove a Ramanujan-type series for Pi?

A question of convergence of a series closely related to two sequences of prime numbers

Intuition: $]0,\infty[: \{x \mapsto \arctan{(nx)}: n \in \mathbb N\}$

Why does Brent/Salamin algorithm double the digits of $\pi$ with each iteration?

Limit of expectation of stochastic process

Convergence of the sequence $x_n= \frac{1}{n+1}+\frac{1}{n+2}+\dots+\frac{1}{2n}$

Why do we have $(1+\frac{c}{n}+o(\frac{1}{n}))^n \to e^c$ as $n \to \infty?$

Number of fixed points converges to poisson distribution?

Prove that $\sum_{k=0}^{\infty}{\frac{(3i)^k}{k!}}$ converges .

Prove the divergence of $\sum_{k=0}^{\infty}{\frac{1}{10k+1}}$

Proof that if $\sum_{n}|f_{n}(z)|$ converges, then $\prod_{n}(1+f_{n}(z))$ converges.

Prove the divergence of $\sum_{k=1}^{\infty}{\frac{k}{\sqrt[3]{k+1}}}$ (Alternative proofs)

Distance from a closed set.

Exercise on pointwise convergence

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