Question

Proof that $\frac{2\times2\times2\times4\times4\cdots(2n)\times(2n)}{3\times3\times5\times5\cdots(2n-1)\times(2n+1)}$ converges to $\frac{\pi}{2}$

score 73 · Answer 1 · 2026-03-28 11:54:05

73

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Proof that $\frac{2\times2\times2\times4\times4\cdots(2n)\times(2n)}{3\times3\times5\times5\cdots(2n-1)\times(2n+1)}$ converges to $\frac{\pi}{2}$

Published on 28 Mar 2026 - 11:54

score 89 · Answer 2 · 2026-04-13 02:05:34

89

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Sum of random variables tilted by Bernoullies

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score 52 · Answer 3 · 2026-04-09 05:29:55

52

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score 213 · Answer 4 · 2019-03-11 19:20:31

213

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score 77 · Answer 5 · 2026-04-09 15:00:58

77

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Steps to determine the interval of continuity of $f(x)= \sum_{n=2}^{\infty} \frac{(\sin{nx})^2}{\sqrt{n}}$

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score 214 · Answer 6 · 2026-04-12 11:53:46

214

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score 35 · Answer 8 · 2026-04-13 04:56:38

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score 117 · Answer 11 · 2019-03-14 10:13:18

117

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score 122 · Answer 12 · 2026-04-12 04:15:22

122

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136

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score 38 · Answer 14 · 2026-03-30 15:15:57

38

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What is the radius of convergence for $\sum_{n=1}^{\infty}(\sqrt[n]{n}+2)^{n}z^{n}$?

Published on 30 Mar 2026 - 15:15

score 35 · Answer 15 · 2026-03-30 15:17:15

35

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For what complex values $z$ make the series $\sum_{n=0}^{\infty}\frac{2}{1+z^{n}}$ converge?

Published on 30 Mar 2026 - 15:17

List Question

Proof that $\frac{2\times2\times2\times4\times4\cdots(2n)\times(2n)}{3\times3\times5\times5\cdots(2n-1)\times(2n+1)}$ converges to $\frac{\pi}{2}$

Sum of random variables tilted by Bernoullies

Does the Weierstrass M-test apply if a term of the functional series is undefined on the domain of definition?

Cluster point of a sequence is limit of a subsequence

Steps to determine the interval of continuity of $f(x)= \sum_{n=2}^{\infty} \frac{(\sin{nx})^2}{\sqrt{n}}$

Baby Rudin ex. 3.8 proof verification

Convergence of the Laplace Exponent of a Compound Poisson Process, Lèvy Fluctuation Theory

I need help showing the first condition of the dominated convergence theorem.

Verification of understanding proving convergence of random variables.

Prove the correctness and continuity of function

Show that if $x_{n}$ converges to $x_0$ , then $Ax_0 = y$

Criteria for almost sure convergence

Abel-Dini-Type Theorem for convergent series

What is the radius of convergence for $\sum_{n=1}^{\infty}(\sqrt[n]{n}+2)^{n}z^{n}$?

For what complex values $z$ make the series $\sum_{n=0}^{\infty}\frac{2}{1+z^{n}}$ converge?

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