List questions from factorial

Published on 20 Feb 2017 - 21:31

358

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Is this a better 'natural' extension of factorials than the Gamma function?

Published on 21 Feb 2017 - 6:07

347

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Same Birthday Probability

Published on 23 Feb 2026 - 14:37

233

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Bounding Values of Large Factorials

Published on 23 Feb 2017 - 18:31

301

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Prove an identity involving factorials inside summations

Published on 31 Mar 2026 - 15:45

14.6k

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Limit of $n$th root of $n$!

Published on 24 Feb 2017 - 21:43

279

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Prove that $\phi=\frac{13}{8} + \sum \limits_{n=0}^{\infty}\frac{(-1)^{(n+1)}(2n+1)!}{n!\,(n+2)!\,4^{(2n+3)}}$.

Published on 26 Mar 2026 - 4:53

83

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Comparing the value of $(1^r + 2^r +3^r +\ ...\ + n^r)^n$ with $(n^n)(n!)^r$, ${(n)^2n}{(n!)^r}$, ${(n)^n}{(n!)^2r}$, ${(n)^n}{(n!)^2r}$

Published on 25 Feb 2017 - 14:19

189

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Closed form for the sums $S(n)={(2n-1)!\over \sqrt2}\cdot{\left(4/ \pi\right)^{2n}}\cdot\sum\limits_{k=0}^{\infty}(-1)^{k(k+1)/2}(2k+1)^{-2n}$

Published on 27 Feb 2017 - 7:04

104

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Why is $ a_n= \frac{(2n)!-2(n!)^2}{(n!)^2n} $ a natural number when $n$ is a prime number?

Published on 01 Mar 2017 - 11:24

313

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How to do counting problems with restrictions

Published on 01 Mar 2017 - 15:30

74

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Counting with restrictions in die throws

Published on 01 Mar 2017 - 17:05

25

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On a certain limit looking as a square root of a factorial function

Published on 05 Mar 2017 - 15:28

80

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What are the stepps to this shortcut?

Published on 05 Mar 2017 - 17:28

957

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How to prove that $(10n+2)!$ is divisible by $(10n+4)$

Published on 05 Mar 2017 - 22:02

List Question

Convergence of infinite series involving factorials

Is this a better 'natural' extension of factorials than the Gamma function?

Same Birthday Probability

Bounding Values of Large Factorials

Prove an identity involving factorials inside summations

Limit of $n$th root of $n$!

Prove that $\phi=\frac{13}{8} + \sum \limits_{n=0}^{\infty}\frac{(-1)^{(n+1)}(2n+1)!}{n!\,(n+2)!\,4^{(2n+3)}}$.

Comparing the value of $(1^r + 2^r +3^r +\ ...\ + n^r)^n$ with $(n^n)(n!)^r$, ${(n)^2n}{(n!)^r}$, ${(n)^n}{(n!)^2r}$, ${(n)^n}{(n!)^2r}$

Closed form for the sums $S(n)={(2n-1)!\over \sqrt2}\cdot{\left(4/ \pi\right)^{2n}}\cdot\sum\limits_{k=0}^{\infty}(-1)^{k(k+1)/2}(2k+1)^{-2n}$

Why is $ a_n= \frac{(2n)!-2(n!)^2}{(n!)^2n} $ a natural number when $n$ is a prime number?

How to do counting problems with restrictions

Counting with restrictions in die throws

On a certain limit looking as a square root of a factorial function

What are the stepps to this shortcut?

How to prove that $(10n+2)!$ is divisible by $(10n+4)$

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