List questions from products

Published on 03 Apr 2026 - 0:19

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Average of products VS. product of averages

Published on 14 Feb 2014 - 3:58

222

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What does $\prod_{n\geq2}\frac{n^4-1}{n^4+1}$ converge to?

Published on 19 Feb 2014 - 2:34

262

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Roots of unity product

Published on 30 Mar 2026 - 4:08

41

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Derivative: Which rule to use first?

Published on 20 Feb 2014 - 18:20

1.8k

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Direct product commutes with direct sum?

Published on 23 Feb 2014 - 4:23

364

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When can we write the square of a matrix as the product of the matrix and its transpose?

Published on 01 Mar 2014 - 2:57

202

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If $a_1a_2\cdots a_n =1$, then $\prod_{i=1}^n (1+a_i) \geq 2^n$

Published on 26 Mar 2026 - 14:21

3.1k

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swap summation and multiple

Published on 06 Mar 2014 - 4:29

70

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Union of Cartesian squares

Published on 06 Mar 2014 - 13:09

77

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If $a\neq 1$, find $(a+1)(a^2+1)(a^4+1)\ldots(a^{2^n}+1)$.

Published on 07 Mar 2014 - 14:51

172

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Prove that $(1-\frac{1}{2^2}\cdots 1-\frac{1}{9\,999^2})(1-\frac{1}{10\,000^2})=0.500\,05$

Published on 07 Mar 2014 - 18:25

14.3k

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How to interchange a sum and a product?

Published on 09 Mar 2014 - 22:43

148

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Compute $\prod_{k=5}^{\infty}\frac{k^4-17k^2+16}{k^4-8k^2+16}$

Published on 01 Apr 2026 - 14:43

60

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$\prod_{k=1}^n k\ \ \equiv 1 \bmod{n}$ where $gcd(k,n)=gcd(k+1,n)=1$

Published on 09 Apr 2017 - 17:17

List Question

Product of standard normal and uniform random variable

Average of products VS. product of averages

What does $\prod_{n\geq2}\frac{n^4-1}{n^4+1}$ converge to?

Roots of unity product

Derivative: Which rule to use first?

Direct product commutes with direct sum?

When can we write the square of a matrix as the product of the matrix and its transpose?

If $a_1a_2\cdots a_n =1$, then $\prod_{i=1}^n (1+a_i) \geq 2^n$

swap summation and multiple

Union of Cartesian squares

If $a\neq 1$, find $(a+1)(a^2+1)(a^4+1)\ldots(a^{2^n}+1)$.

Prove that $(1-\frac{1}{2^2}\cdots 1-\frac{1}{9\,999^2})(1-\frac{1}{10\,000^2})=0.500\,05$

How to interchange a sum and a product?

Compute $\prod_{k=5}^{\infty}\frac{k^4-17k^2+16}{k^4-8k^2+16}$

$\prod_{k=1}^n k\ \ \equiv 1 \bmod{n}$ where $gcd(k,n)=gcd(k+1,n)=1$

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