Question

A comparison test for uniform convergence -- counterexample

score 249 · Answer 1 · 2026-04-16 01:08:01

249

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A comparison test for uniform convergence -- counterexample

Published on 16 Apr 2026 - 1:08

score 94 · Answer 2 · 2026-04-11 03:46:17

94

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How to show that $ \langle \sqrt n \rangle $ is not converging

Published on 11 Apr 2026 - 3:46

score 134 · Answer 3 · 2026-04-17 03:03:08

134

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Given $x_1 \colon=1$, $x_2 \colon=2$, and $x_n\colon=\left( x_{n-1}+x_{n-2}\right)/2$, how to establish this relation?

Published on 17 Apr 2026 - 3:03

score 62 · Answer 4 · 2026-04-15 22:45:23

62

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Is there a strictly-decreasing sequence $(x_n)$ with $x_n \rightarrow 0$ and $\frac{x_{n+1}}{x_n}\rightarrow1$?

Published on 15 Apr 2026 - 22:45

score 170 · Answer 5 · 2026-04-16 04:31:10

170

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Proof Verification: Regarding equivalent sequences and Cauchy sequences, Tao Analysis I: Exercise 5.2.1.

Published on 16 Apr 2026 - 4:31

score 53 · Answer 6 · 2026-04-11 09:32:35

53

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Finding a bound of rational sequence for a sequence converging to zero

Published on 11 Apr 2026 - 9:32

score 91 · Answer 7 · 2026-04-09 16:22:58

91

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Getting the volume of a sphere from an infinite product

Published on 09 Apr 2026 - 16:22

score 38 · Answer 8 · 2026-04-08 01:09:42

38

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Reorder an infinite series to start from infinity

Published on 08 Apr 2026 - 1:09

score 407 · Answer 9 · 2026-04-12 18:09:39

407

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When is the product of limsups equal to the limsup of the products?

Published on 12 Apr 2026 - 18:09

score 319 · Answer 10 · 2026-04-14 21:47:10

319

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Prove $\sum\limits_{n=2}^\infty \frac {1} {n\ln(n)\sqrt{\ln^3{n}}}$ is divergent.

Published on 14 Apr 2026 - 21:47

score 165 · Answer 11 · 2026-04-23 00:40:57

165

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Show that $|A+A| < 2.5 |A| $ with $A = \{ [n \sqrt{2}] : 1 \leq n \leq N \}$

Published on 23 Apr 2026 - 0:40

score 177 · Answer 12 · 2026-03-26 01:04:42

177

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Why do expressions of the form $\sum\limits^\infty_{n=1} \frac{n^k}{3^n}$ sum 'nicely'?

Published on 26 Mar 2026 - 1:04

score 106 · Answer 13 · 2026-04-15 11:33:46

106

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Prove $\lim_{m\to\infty}\sum_{k=1}^m\frac{2^{-k}}{k} = \log 2$

Published on 15 Apr 2026 - 11:33

score 74 · Answer 14 · 2026-04-16 10:42:59

74

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If $p > 0$, show that the series $\sum_{n=1}^{\infty} \frac {n!}{p(p+1) \cdots (p+n-1)}$ converges for $p > 2$ and diverges for $p \le 2$

Published on 16 Apr 2026 - 10:42

score 16 · Answer 15 · 2026-04-25 04:36:41

16

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Summation of series of variable degrees...

Published on 25 Apr 2026 - 4:36

List Question

A comparison test for uniform convergence -- counterexample

How to show that $ \langle \sqrt n \rangle $ is not converging

Given $x_1 \colon=1$, $x_2 \colon=2$, and $x_n\colon=\left( x_{n-1}+x_{n-2}\right)/2$, how to establish this relation?

Is there a strictly-decreasing sequence $(x_n)$ with $x_n \rightarrow 0$ and $\frac{x_{n+1}}{x_n}\rightarrow1$?

Proof Verification: Regarding equivalent sequences and Cauchy sequences, Tao Analysis I: Exercise 5.2.1.

Finding a bound of rational sequence for a sequence converging to zero

Getting the volume of a sphere from an infinite product

Reorder an infinite series to start from infinity

When is the product of limsups equal to the limsup of the products?

Prove $\sum\limits_{n=2}^\infty \frac {1} {n\ln(n)\sqrt{\ln^3{n}}}$ is divergent.

Show that $|A+A| < 2.5 |A| $ with $A = \{ [n \sqrt{2}] : 1 \leq n \leq N \}$

Why do expressions of the form $\sum\limits^\infty_{n=1} \frac{n^k}{3^n}$ sum 'nicely'?

Prove $\lim_{m\to\infty}\sum_{k=1}^m\frac{2^{-k}}{k} = \log 2$

If $p > 0$, show that the series $\sum_{n=1}^{\infty} \frac {n!}{p(p+1) \cdots (p+n-1)}$ converges for $p > 2$ and diverges for $p \le 2$

Summation of series of variable degrees...

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