List questions from factorial

Published on 14 Jan 2015 - 17:44

91

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Proving $ n! \geq 2^{n-1} $

Published on 18 Jan 2015 - 12:36

133

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Limit of $\frac{1}{n}\log({n\choose np})$ without using Stirling's formula

Published on 29 Mar 2026 - 5:50

80

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Is there a way to express $(n-i)!(n-j)!(2i)!(2j)!$ in terms of $n$ and $r=i+j$?

Published on 20 Jan 2015 - 3:13

178

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Proving $\frac{((2n)!)^2(i)!(j)!}{((n)!)^2(2i)!(2j)!}$ is an integer

Published on 20 Jan 2015 - 4:04

244

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Simplifying factorials

Published on 20 Jan 2015 - 12:25

1.5k

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Proving an identity involving factorials

Published on 21 Jan 2015 - 1:53

288

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Inequality $(n!)^2\le \left[\frac{(n+1)(n+2)}{6}\right]^n$

Published on 21 Jan 2015 - 3:35

135

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$x!=y^n$ for $x,y \neq 0,1$

Published on 21 Jan 2015 - 18:14

303

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Finding the largest factorial with only three distinct decimal digits

Published on 23 Jan 2015 - 8:44

1.5k

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In how many ways can the word "WORD" be rearranged so that no letter is in its original position?

Published on 24 Jan 2015 - 4:57

111

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Factorial formula problem

Published on 25 Jan 2015 - 17:22

72

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Prove for any integer $N$ that there exists $n > N$ where $n!-1$ is not a prime

Published on 26 Jan 2015 - 0:33

264

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Cannot follow proof that $n! \leq en(n/e)^n$

Published on 26 Jan 2015 - 18:52

98

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Computing $\mathrm{gcd} (100!, 3^{100})$

Published on 26 Jan 2015 - 22:15

List Question

Evaluate: $\sum_{k=2}^n\frac {n!}{(n-k)!(k-2)!}$

Proving $ n! \geq 2^{n-1} $

Limit of $\frac{1}{n}\log({n\choose np})$ without using Stirling's formula

Is there a way to express $(n-i)!(n-j)!(2i)!(2j)!$ in terms of $n$ and $r=i+j$?

Proving $\frac{((2n)!)^2(i)!(j)!}{((n)!)^2(2i)!(2j)!}$ is an integer

Simplifying factorials

Proving an identity involving factorials

Inequality $(n!)^2\le \left[\frac{(n+1)(n+2)}{6}\right]^n$

$x!=y^n$ for $x,y \neq 0,1$

Finding the largest factorial with only three distinct decimal digits

In how many ways can the word "WORD" be rearranged so that no letter is in its original position?

Factorial formula problem

Prove for any integer $N$ that there exists $n > N$ where $n!-1$ is not a prime

Cannot follow proof that $n! \leq en(n/e)^n$

Computing $\mathrm{gcd} (100!, 3^{100})$

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