Question

Finding the value of the infinite product $\prod\limits_{n=1}^{\infty} \biggl(1-\frac{1}{2^{n}}\biggr)$

score 53 · Answer 1 · 2026-04-03 05:19:20

53

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Finding the value of the infinite product $\prod\limits_{n=1}^{\infty} \biggl(1-\frac{1}{2^{n}}\biggr)$

Published on 03 Apr 2026 - 5:19

score 57 · Answer 2 · 2026-04-02 22:41:07

57

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Calculate $(i+u_0)(i+u_1)\cdots(i+u_{n-1})$ if $u_0,u_1,...u_{n-1}$ are $n-$th roots of unity

Published on 02 Apr 2026 - 22:41

score 105 · Answer 3 · 2026-03-28 10:16:35

105

Views

Can we find a palindrome for more than $5$ factors?

Published on 28 Mar 2026 - 10:16

score 186 · Answer 4 · 2021-12-26 18:50:15

If a product exists for a set of objects in a category, then is there a product in the category for every subset of those objects?

score 61 · Answer 5 · 2026-03-26 01:03:06

61

Views

Maxima CAS: How to force log() into a product?

Published on 26 Mar 2026 - 1:03

score 200 · Answer 6 · 2026-04-05 12:09:23

200

Views

Could there be an irrational number $x$ such that the product of $x$ and $\pi$ are rational?

Published on 05 Apr 2026 - 12:09

score 192 · Answer 7 · 2022-01-05 12:02:18

192

Views

I wish to solve exactly this formula involving sums and products

Published on 05 Jan 2022 - 12:02

score 121 · Answer 8 · 2022-01-09 12:38:37

121

Views

Is there a simple way to expand the following Product Sum?

Published on 09 Jan 2022 - 12:38

score 73 · Answer 9 · 2022-01-09 19:01:57

73

Views

How to simplify properly this product?

Published on 09 Jan 2022 - 19:01

score 138 · Answer 10 · 2026-03-30 04:57:34

138

Views

Describe all path-connected $3$ fold covers of $X=S^1 \vee \mathbb{R}P^2$

Published on 30 Mar 2026 - 4:57

score 37 · Answer 11 · 2022-01-19 09:55:06

37

Views

Summation over permutations

Published on 19 Jan 2022 - 9:55

score 47 · Answer 12 · 2022-01-20 13:13:40

Prove $\lim _{n \rightarrow \infty} \prod_{i=1}^{n+1} \cos \frac{\sqrt{2 i-1}}{n} a^{2}=\mathrm{e}^{-\frac{a^{4}}{2}}$ using the "fitting method"

score 284 · Answer 13 · 2026-04-02 04:32:40

284

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If $\alpha,\beta,\gamma$ are the roots of $x^3+x^2-x+1=0$, find the value of $\prod\left(\frac1{\alpha^3}+\frac1{\beta^3}-\frac1{\gamma^3}\right)$

Published on 02 Apr 2026 - 4:32

score 48 · Answer 14 · 2022-01-26 00:04:56

48

Views

Simplify product of two product operators

Published on 26 Jan 2022 - 0:04

score 709 · Answer 15 · 2022-01-26 14:52:00

709

Views

Multiplication of 3D matrix by 2D matrix in Matlab without using loops

Published on 26 Jan 2022 - 14:52

List Question

Finding the value of the infinite product $\prod\limits_{n=1}^{\infty} \biggl(1-\frac{1}{2^{n}}\biggr)$

Calculate $(i+u_0)(i+u_1)\cdots(i+u_{n-1})$ if $u_0,u_1,...u_{n-1}$ are $n-$th roots of unity

Can we find a palindrome for more than $5$ factors?

If a product exists for a set of objects in a category, then is there a product in the category for every subset of those objects?

Maxima CAS: How to force log() into a product?

Could there be an irrational number $x$ such that the product of $x$ and $\pi$ are rational?

I wish to solve exactly this formula involving sums and products

Is there a simple way to expand the following Product Sum?

How to simplify properly this product?

Describe all path-connected $3$ fold covers of $X=S^1 \vee \mathbb{R}P^2$

Summation over permutations

Prove $\lim _{n \rightarrow \infty} \prod_{i=1}^{n+1} \cos \frac{\sqrt{2 i-1}}{n} a^{2}=\mathrm{e}^{-\frac{a^{4}}{2}}$ using the "fitting method"

If $\alpha,\beta,\gamma$ are the roots of $x^3+x^2-x+1=0$, find the value of $\prod\left(\frac1{\alpha^3}+\frac1{\beta^3}-\frac1{\gamma^3}\right)$

Simplify product of two product operators

Multiplication of 3D matrix by 2D matrix in Matlab without using loops

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