Question

Finding $ \lim_{n \rightarrow \infty} \prod_{j=1}^n \frac{2j-1}{2j}$

score 157 · Answer 1 · 2014-12-25 08:25:57

157

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Finding $ \lim_{n \rightarrow \infty} \prod_{j=1}^n \frac{2j-1}{2j}$

Published on 25 Dec 2014 - 8:25

score 1k · Answer 2 · 2026-03-25 23:11:02

1k

Views

Calculate $\sqrt{\frac{1}{2}} \times \sqrt{\frac{1}{2} + \frac{1}{2}\sqrt{\frac{1}{2}}} \times \ldots $

Published on 25 Mar 2026 - 23:11

score 195 · Answer 3 · 2026-03-25 12:50:50

195

Views

The limit of an infinite product involving the squares of $\binom{n}{j}x^j(1-x)^{n-j}/k$

Published on 25 Mar 2026 - 12:50

score 180 · Answer 4 · 2014-12-30 11:25:38

180

Views

Infinite product for a generalization of gamma function

Published on 30 Dec 2014 - 11:25

score 233 · Answer 5 · 2014-12-31 22:07:56

233

Views

Proving the inequality $ \left|\prod_{i=0}^n \left(x - \frac{i}{n}\right)\right| \le \frac{n!}{4n^{n+1}}$

Published on 31 Dec 2014 - 22:07

score 860 · Answer 6 · 2026-03-25 06:12:48

860

Views

What is the product of $p_i-1 \over p_i$

Published on 25 Mar 2026 - 6:12

score 38 · Answer 7 · 2019-10-02 14:35:28

38

Views

How do I check convergence of an infinite product divided by an infinite sum /// Is it possible?

Published on 02 Oct 2019 - 14:35

score 196 · Answer 8 · 2019-10-08 00:20:30

196

Views

Studying the convergence of an infinite product.

Published on 08 Oct 2019 - 0:20

score 191 · Answer 9 · 2019-10-09 14:46:06

191

Views

Formula for $\prod\limits_{k=-\infty}^\infty \frac{1}{e}\left(1+\frac{1}{k+z}\right)^{k+z+\frac{1}{2}}$

Published on 09 Oct 2019 - 14:46

score 125 · Answer 10 · 2019-10-11 00:14:01

125

Views

Prove that $\sum_{n=0}^\infty\frac{x^{2n+1}}{1+x^{4n+2}}\neq0$ for complex $x$

Published on 11 Oct 2019 - 0:14

score 180 · Answer 11 · 2019-10-14 03:28:51

180

Views

Closed form of infinite product

Published on 14 Oct 2019 - 3:28

score 340 · Answer 12 · 2026-03-22 12:12:22

340

Views

Box topology and a non-continuous function

Published on 22 Mar 2026 - 12:12

score 77 · Answer 13 · 2019-11-13 18:55:42

77

Views

Convergence of logs imply convergence of series

Published on 13 Nov 2019 - 18:55

score 86 · Answer 14 · 2019-11-13 22:41:49

86

Views

How to show that $a_n = (1+\frac12)(1+\frac14)\cdots(1+\frac1{2^n})$ converges?

Published on 13 Nov 2019 - 22:41

score 70 · Answer 15 · 2019-11-19 04:50:44

70

Views

Maximum and minimum for $f(z)=z^m \Pi_n (1-z/a_n)$ and $g(z)=z^m \Pi_n(1-z/|a_n|)$

Published on 19 Nov 2019 - 4:50

List Question

Finding $ \lim_{n \rightarrow \infty} \prod_{j=1}^n \frac{2j-1}{2j}$

Calculate $\sqrt{\frac{1}{2}} \times \sqrt{\frac{1}{2} + \frac{1}{2}\sqrt{\frac{1}{2}}} \times \ldots $

The limit of an infinite product involving the squares of $\binom{n}{j}x^j(1-x)^{n-j}/k$

Infinite product for a generalization of gamma function

Proving the inequality $ \left|\prod_{i=0}^n \left(x - \frac{i}{n}\right)\right| \le \frac{n!}{4n^{n+1}}$

What is the product of $p_i-1 \over p_i$

How do I check convergence of an infinite product divided by an infinite sum /// Is it possible?

Studying the convergence of an infinite product.

Formula for $\prod\limits_{k=-\infty}^\infty \frac{1}{e}\left(1+\frac{1}{k+z}\right)^{k+z+\frac{1}{2}}$

Prove that $\sum_{n=0}^\infty\frac{x^{2n+1}}{1+x^{4n+2}}\neq0$ for complex $x$

Closed form of infinite product

Box topology and a non-continuous function

Convergence of logs imply convergence of series

How to show that $a_n = (1+\frac12)(1+\frac14)\cdots(1+\frac1{2^n})$ converges?

Maximum and minimum for $f(z)=z^m \Pi_n (1-z/a_n)$ and $g(z)=z^m \Pi_n(1-z/|a_n|)$

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