Question

Computing $\lim_{n\to \infty}{\frac{5\cdot9\cdot13\cdot\dots.\cdot(4n+1)}{7\cdot11\cdot15\cdot\dots.\cdot(4n+3)}}$

score 1.7k · Answer 1 · 2014-01-15 18:18:29

1.7k

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Computing $\lim_{n\to \infty}{\frac{5\cdot9\cdot13\cdot\dots.\cdot(4n+1)}{7\cdot11\cdot15\cdot\dots.\cdot(4n+3)}}$

Published on 15 Jan 2014 - 18:18

score 355 · Answer 2 · 2014-01-19 10:10:54

355

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Convergence condition of infinite cosine product

Published on 19 Jan 2014 - 10:10

score 851 · Answer 3 · 2014-01-24 10:09:47

851

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Finding limit of a sequence in product form

Published on 24 Jan 2014 - 10:09

score 144 · Answer 4 · 2014-01-28 23:11:55

144

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$\frac{f'(z)}{f(z)}= \sum_{n=1}^{+ \infty}\frac{f'_{n}(z)}{f_{n}(z)}$

Published on 28 Jan 2014 - 23:11

score 87 · Answer 5 · 2014-01-29 07:39:05

87

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$\prod_{n}f_{n}$ converges uniformly $\Rightarrow $ $\sum_{n}\mathrm{Log}(f_{n})$ converges uniformly

Published on 29 Jan 2014 - 7:39

score 154 · Answer 6 · 2014-02-02 18:33:16

154

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Comparison between infinite products and series

Published on 02 Feb 2014 - 18:33

score 87 · Answer 7 · 2014-02-03 14:04:33

87

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Finding limit of $\prod_{t=1}^{n}{\left(1-\frac{2}{(n)(n+1)}\right)^2}$

Published on 03 Feb 2014 - 14:04

score 903 · Answer 8 · 2026-03-30 07:06:19

903

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Proof that the series for the generating function of the partition function converges?

Published on 30 Mar 2026 - 7:06

score 116 · Answer 9 · 2014-02-08 07:28:30

116

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How do I prove $\lim_{n\to\infty} \frac{n^z n!}{z(z+1)\cdots (z+n)}=\frac{1}{z}\prod_{n=1}^\infty \frac{(1+\frac{1}{n})^z}{1+\frac{z}{n}}$?

Published on 08 Feb 2014 - 7:28

score 925 · Answer 10 · 2014-02-09 04:10:52

925

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Infinite product of sinc functions

Published on 09 Feb 2014 - 4:10

score 274 · Answer 11 · 2014-02-12 08:10:34

274

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$\prod_{i=1}^{\infty}{1+(\frac{k}{i})^3}$ for integer k

Published on 12 Feb 2014 - 8:10

score 564 · Answer 12 · 2014-02-13 03:47:36

564

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How find this $\prod_{n=2}^{\infty}\left(1-\frac{1}{n^6}\right)$

Published on 13 Feb 2014 - 3:47

score 118 · Answer 13 · 2014-02-13 06:31:03

118

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Can someone walk me through this infinite product?

Published on 13 Feb 2014 - 6:31

score 503 · Answer 14 · 2014-02-17 10:58:36

503

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Evaluate these infinite products $\prod_{n\geq 2}(1-\frac{1}{n^3})$ and $\prod_{n\geq 1}(1+\frac{1}{n^3})$

Published on 17 Feb 2014 - 10:58

score 958 · Answer 15 · 2014-02-18 23:04:38

958

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Proof of convergence of an infinite product

Published on 18 Feb 2014 - 23:04

List Question

Computing $\lim_{n\to \infty}{\frac{5\cdot9\cdot13\cdot\dots.\cdot(4n+1)}{7\cdot11\cdot15\cdot\dots.\cdot(4n+3)}}$

Convergence condition of infinite cosine product

Finding limit of a sequence in product form

$\frac{f'(z)}{f(z)}= \sum_{n=1}^{+ \infty}\frac{f'_{n}(z)}{f_{n}(z)}$

$\prod_{n}f_{n}$ converges uniformly $\Rightarrow $ $\sum_{n}\mathrm{Log}(f_{n})$ converges uniformly

Comparison between infinite products and series

Finding limit of $\prod_{t=1}^{n}{\left(1-\frac{2}{(n)(n+1)}\right)^2}$

Proof that the series for the generating function of the partition function converges?

How do I prove $\lim_{n\to\infty} \frac{n^z n!}{z(z+1)\cdots (z+n)}=\frac{1}{z}\prod_{n=1}^\infty \frac{(1+\frac{1}{n})^z}{1+\frac{z}{n}}$?

Infinite product of sinc functions

$\prod_{i=1}^{\infty}{1+(\frac{k}{i})^3}$ for integer k

How find this $\prod_{n=2}^{\infty}\left(1-\frac{1}{n^6}\right)$

Can someone walk me through this infinite product?

Evaluate these infinite products $\prod_{n\geq 2}(1-\frac{1}{n^3})$ and $\prod_{n\geq 1}(1+\frac{1}{n^3})$

Proof of convergence of an infinite product

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