List questions from factorial

Published on 28 Feb 2014 - 9:33

1.9k

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Even or Odd for factorial

Published on 01 Mar 2014 - 6:39

670

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$\frac{x}{10!} = \frac{1}{8!} + \frac{1}{9!}$

Published on 05 Apr 2026 - 9:03

277

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Evaluating $\lim_{n\to \infty}\frac1{2n}\log\left({2n \choose n}\right)$

Published on 06 Mar 2014 - 6:43

451

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Prove $\sum_{n=1}^\infty(e-\sum_{k=0}^n\frac1{k!})=1$

Published on 07 Mar 2014 - 17:57

834

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Relation/connection between $n!$ or $e$ and $2^n$

Published on 09 Mar 2014 - 16:35

658

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Proving an inequality involving factorials: $(\frac{n}{2})^n \ge n! \geq (\frac{n}{3})^n$

Published on 09 Mar 2014 - 17:03

116.6k

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Calculating the limit $\lim((n!)^{1/n})$

Published on 10 Mar 2014 - 8:15

313

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How to show $\sum_{i=1}^{n} \binom{i}{2}=\binom{n+1}{3}$?

Published on 10 Mar 2014 - 21:25

64

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$\sum_{i=1}^{n}i^k=\sum_{i=1}^{k}\frac{c_{k+1-i}k!}{i!}n^i$. What is known about $\{c_k\}_{k=0}^{\infty}$?

Published on 04 Apr 2026 - 3:56

221

Views

Factorial: product over primes

Published on 07 Apr 2026 - 11:12

314

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Showing that $10!=6!7!$ via Gamma function

Published on 07 Apr 2026 - 11:12

60

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Are these the only solutions to $a!b!=c!$?

Published on 11 Apr 2017 - 13:23

74

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Evaluating the closed form for $\int_{0}^{\infty}\ln^k\left({1+{1\over x}}\right) \cdot{\mathrm dx\over (1+x)^n}=F(k,n)$

Published on 11 Apr 2017 - 19:59

142

Views

Proof without induction : $(n+1)! < n(1!+2!+\cdots +n!)$

Published on 13 Apr 2017 - 18:20

List Question

Mathematical Induction Proof: $\sum_{i=1}^n$ $(i \times i!) = (n+1)! - 1$

Even or Odd for factorial

$\frac{x}{10!} = \frac{1}{8!} + \frac{1}{9!}$

Evaluating $\lim_{n\to \infty}\frac1{2n}\log\left({2n \choose n}\right)$

Prove $\sum_{n=1}^\infty(e-\sum_{k=0}^n\frac1{k!})=1$

Relation/connection between $n!$ or $e$ and $2^n$

Proving an inequality involving factorials: $(\frac{n}{2})^n \ge n! \geq (\frac{n}{3})^n$

Calculating the limit $\lim((n!)^{1/n})$

How to show $\sum_{i=1}^{n} \binom{i}{2}=\binom{n+1}{3}$?

$\sum_{i=1}^{n}i^k=\sum_{i=1}^{k}\frac{c_{k+1-i}k!}{i!}n^i$. What is known about $\{c_k\}_{k=0}^{\infty}$?

Factorial: product over primes

Showing that $10!=6!7!$ via Gamma function

Are these the only solutions to $a!b!=c!$?

Evaluating the closed form for $\int_{0}^{\infty}\ln^k\left({1+{1\over x}}\right) \cdot{\mathrm dx\over (1+x)^n}=F(k,n)$

Proof without induction : $(n+1)! < n(1!+2!+\cdots +n!)$

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