List questions from factorial

Published on 26 Mar 2026 - 4:51

208

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Factorials with fractions

Published on 25 Oct 2014 - 22:32

388

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Equal products of consecutive integers

Published on 26 Oct 2014 - 13:19

1k

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How can I show that $n! \leqslant \left(\frac{n+1}{2}\right)^n$?

Published on 26 Oct 2014 - 17:14

324

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Prove that $n! > n^5$

Published on 26 Oct 2014 - 22:05

100

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Prove $(n!)/n^n \leq 1/2^{k}$, where $k$ is the floor of $n/2$.

Published on 27 Mar 2026 - 11:48

261

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Primality of $n! +1$

Published on 26 Mar 2026 - 9:26

13.7k

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How to calculate decimal factorials, like $0.78!$

Published on 28 Oct 2014 - 14:59

1.1k

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Using the squeeze theorem to determine a limit $\lim_{n\to\infty} (n!)^{\frac{1}{n^2}}$

Published on 28 Oct 2014 - 19:50

1.6k

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Is there a Sum Factorial?

Published on 29 Oct 2014 - 2:45

305

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Compute largest integer power of $6$ that divides $73!$

Published on 29 Oct 2014 - 12:56

186

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Proving that $\sum_{k=0}^\infty\frac{2^{-5k}(6k+1)((2k-1)!!)^3}{4(k!)^3} = {1\over\pi}$

Published on 25 Mar 2026 - 16:02

208

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Is this a demonstration or a definition?

Published on 29 Oct 2014 - 20:57

350

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Proving that $(3n)!$ is divisible by $n! \times (n + 1)! \times (n + 2)!$ if $n$ is greater than 2

Published on 01 Nov 2014 - 9:44

286

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Proving that $\lim\limits_{n \to \infty}\frac{5^n}{n!} = 0$

Published on 01 Nov 2014 - 20:41

List Question

How to evaluate factorials greater than $69!$

Factorials with fractions

Equal products of consecutive integers

How can I show that $n! \leqslant \left(\frac{n+1}{2}\right)^n$?

Prove that $n! > n^5$

Prove $(n!)/n^n \leq 1/2^{k}$, where $k$ is the floor of $n/2$.

Primality of $n! +1$

How to calculate decimal factorials, like $0.78!$

Using the squeeze theorem to determine a limit $\lim_{n\to\infty} (n!)^{\frac{1}{n^2}}$

Is there a Sum Factorial?

Compute largest integer power of $6$ that divides $73!$

Proving that $\sum_{k=0}^\infty\frac{2^{-5k}(6k+1)((2k-1)!!)^3}{4(k!)^3} = {1\over\pi}$

Is this a demonstration or a definition?

Proving that $(3n)!$ is divisible by $n! \times (n + 1)! \times (n + 2)!$ if $n$ is greater than 2

Proving that $\lim\limits_{n \to \infty}\frac{5^n}{n!} = 0$

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