List questions from factorial

Published on 18 Nov 2017 - 0:00

262

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I dont understand this combinatorial proof

Published on 19 Nov 2017 - 9:56

197

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Closed-form summation of $\sum_{i=1}^n i\frac{x^i}{i!}$

Published on 26 Mar 2026 - 8:00

124

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How to reduce following expression so that it less computation.

Published on 21 Nov 2017 - 15:24

51

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How to show that $\dfrac {n!}{(n-k)!} \leq n^{k}$

Published on 21 Nov 2017 - 22:08

805

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How to show inductively that $(2n)! > (n!)^2$

Published on 21 Nov 2017 - 22:11

46

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Remainder of Summation Modulo $992$

Published on 23 Nov 2017 - 20:19

153

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How do I calculate F if both sides have factorials?

Published on 08 Apr 2026 - 10:10

82

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I found a correlation between n^x and x! can anyone explain it?

Published on 24 Nov 2017 - 19:31

2.1k

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Find smallest positive integer $n$ such that $n!$ is divisible by $p^k$ ($p =$ positive prime, $k =$ positive integer)

Published on 03 Apr 2026 - 10:37

64

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Approximating $e^x$ to 16 decimal places within given interval $ x \in (-\frac{1}{2},\frac{1}{2})$

Published on 26 Nov 2017 - 16:50

86

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How to solve a binomial for $n$

Published on 05 Apr 2026 - 17:13

215

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$\frac{(2n − 1)!!}{(2n)!!} \leq \frac{1}{\sqrt{2n+1}}$ by induction?

Published on 03 Apr 2026 - 19:38

2.6k

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Express Product of an Arithmetic Sequence in Terms of Factorials

Published on 30 Mar 2026 - 4:25

279

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$\lim_{n\to\infty} \sum_{k=1}^n \frac{k!}{n!}$

Published on 23 Feb 2026 - 7:56

List Question

Formula for Partial Deranged Matchings

I dont understand this combinatorial proof

Closed-form summation of $\sum_{i=1}^n i\frac{x^i}{i!}$

How to reduce following expression so that it less computation.

How to show that $\dfrac {n!}{(n-k)!} \leq n^{k}$

How to show inductively that $(2n)! > (n!)^2$

Remainder of Summation Modulo $992$

How do I calculate F if both sides have factorials?

I found a correlation between n^x and x! can anyone explain it?

Find smallest positive integer $n$ such that $n!$ is divisible by $p^k$ ($p =$ positive prime, $k =$ positive integer)

Approximating $e^x$ to 16 decimal places within given interval $ x \in (-\frac{1}{2},\frac{1}{2})$

How to solve a binomial for $n$

$\frac{(2n − 1)!!}{(2n)!!} \leq \frac{1}{\sqrt{2n+1}}$ by induction?

Express Product of an Arithmetic Sequence in Terms of Factorials

$\lim_{n\to\infty} \sum_{k=1}^n \frac{k!}{n!}$

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