Question

Interesting & beautiful Series/Products/Nested Radicals/Continued Fractions

score 140 · Answer 1 · 2026-04-01 10:29:58

140

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Interesting & beautiful Series/Products/Nested Radicals/Continued Fractions

Published on 01 Apr 2026 - 10:29

score 64 · Answer 2 · 2026-03-27 16:26:54

64

Views

Modulus of Infinite Product

Published on 27 Mar 2026 - 16:26

score 117 · Answer 3 · 2020-10-28 14:59:28

117

Views

Evaluate $\prod_{k=1}^{\infty}\left(2\cos\left(\frac{\pi}{3^{k+1}}\right)-1\right)$ from polynomial

Published on 28 Oct 2020 - 14:59

score 80 · Answer 4 · 2020-10-30 08:05:32

80

Views

Infinite products $\prod_{n=1}^\infty\sin\frac1n$ and $\prod_{n=1}^\infty\cos\frac1n$

Published on 30 Oct 2020 - 8:05

score 91 · Answer 5 · 2020-10-30 19:44:28

91

Views

Does $\prod_{n=1}^\infty\left(1+\frac{1}{p_n}\right)$ diverge?

Published on 30 Oct 2020 - 19:44

score 649 · Answer 6 · 2020-11-08 23:41:53

649

Views

Infinite product of $\sqrt{2}$

Published on 08 Nov 2020 - 23:41

score 29 · Answer 7 · 2020-11-11 04:30:47

29

Views

Product of absolute values nonzero implies sum of one minus absolute value is bounded

Published on 11 Nov 2020 - 4:30

score 769 · Answer 8 · 2020-11-12 18:22:39

769

Views

Limit of infinite product $ \lim_{x\to 1^-} \prod_{n=0}^{\infty } \left(\frac{1+x^{n+1}}{1+x^n}\right)^{x^n}$

Published on 12 Nov 2020 - 18:22

score 71 · Answer 9 · 2020-11-13 22:52:18

71

Views

Let $x$ be a real number such that $|x|<1$. Determine $\lim_{n \to \infty} \prod_{i=1}^{n} \left(1+x^{2^{i}}\right)$

Published on 13 Nov 2020 - 22:52

score 181 · Answer 10 · 2020-11-17 04:07:22

181

Views

Can the Infinite Product $\prod_{n=1}^\infty \frac{a_n}{a_n + 1}$ Converge or Diverge to Zero?

Published on 17 Nov 2020 - 4:07

score 74 · Answer 11 · 2020-11-21 02:33:16

74

Views

Integral over bounded $V$: $\idotsint _V\prod_{i=1}^{n}x_i^{a_i-1}d^nx$

Published on 21 Nov 2020 - 2:33

score 167 · Answer 12 · 2020-11-23 16:11:39

167

Views

Limit of a product with growing number of factors

Published on 23 Nov 2020 - 16:11

score 228 · Answer 13 · 2020-11-27 00:52:26

228

Views

What kind of mathematical rule was broken in here?

Published on 27 Nov 2020 - 0:52

score 34 · Answer 14 · 2026-03-25 23:24:23

34

Views

Convergence/divergence of sum of finite products of functions of reciprocals of natural numbers

Published on 25 Mar 2026 - 23:24

score 456 · Answer 15 · 2020-12-01 00:20:05

456

Views

Generalizing two infinite products for $\operatorname{sinc}(x)$ and their 'dual' infinite product

Published on 01 Dec 2020 - 0:20

List Question

Interesting & beautiful Series/Products/Nested Radicals/Continued Fractions

Modulus of Infinite Product

Evaluate $\prod_{k=1}^{\infty}\left(2\cos\left(\frac{\pi}{3^{k+1}}\right)-1\right)$ from polynomial

Infinite products $\prod_{n=1}^\infty\sin\frac1n$ and $\prod_{n=1}^\infty\cos\frac1n$

Does $\prod_{n=1}^\infty\left(1+\frac{1}{p_n}\right)$ diverge?

Infinite product of $\sqrt{2}$

Product of absolute values nonzero implies sum of one minus absolute value is bounded

Limit of infinite product $ \lim_{x\to 1^-} \prod_{n=0}^{\infty } \left(\frac{1+x^{n+1}}{1+x^n}\right)^{x^n}$

Let $x$ be a real number such that $|x|<1$. Determine $\lim_{n \to \infty} \prod_{i=1}^{n} \left(1+x^{2^{i}}\right)$

Can the Infinite Product $\prod_{n=1}^\infty \frac{a_n}{a_n + 1}$ Converge or Diverge to Zero?

Integral over bounded $V$: $\idotsint _V\prod_{i=1}^{n}x_i^{a_i-1}d^nx$

Limit of a product with growing number of factors

What kind of mathematical rule was broken in here?

Convergence/divergence of sum of finite products of functions of reciprocals of natural numbers

Generalizing two infinite products for $\operatorname{sinc}(x)$ and their 'dual' infinite product

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