List questions from factorial

Published on 03 Apr 2026 - 7:27

274

Views

Prove that $\lim _{x\to \infty \:}(1+\frac{x^x}{x!})^{\frac{1}{x}} = e$

Published on 04 Apr 2026 - 7:03

228

Views

Prove that $\frac{(n+1)!}{(n-1)!}=n(n+1)$

Published on 28 Feb 2016 - 17:24

73

Views

How can I test the convergence of the following sequence with odd products over even ones?

Published on 01 Mar 2016 - 1:48

90

Views

Minimize $x$ in factorial division

Published on 01 Mar 2016 - 3:26

980

Views

Upper Bound on ${n \choose r} $

Published on 01 Mar 2016 - 3:27

211

Views

Is there a geometrical interpretation of this equality $2\cdot 4\cdot 6\cdot\ldots\cdot(2n)=2^nn!$?

Published on 01 Mar 2016 - 4:13

458

Views

Limit of the spherical Bessel function of the second kind

Published on 01 Apr 2026 - 15:52

103

Views

Does it make sense to multiply probabilities?

Published on 03 Mar 2016 - 2:03

65

Views

Factorials and equivalency

Published on 03 Mar 2016 - 3:08

197

Views

What is $\int\limits_{0}^{1} \left[x(1-x)\right]^m \, dx$ ($m$ positive integer)?

Published on 03 Apr 2026 - 8:54

410

Views

How to prove this gamma identity?

Published on 04 Mar 2016 - 8:09

79

Views

Help required to compute logic of an answer.

Published on 26 Mar 2026 - 9:39

156

Views

How to prove that $(p^2)!$ is divisible by $(p!)^{p+1}$?

Published on 04 Mar 2016 - 19:22

283

Views

Excluding interval from N

Published on 07 Mar 2016 - 19:16

List Question

Calculate chosen element of this Number Pyramid

Prove that $\lim _{x\to \infty \:}(1+\frac{x^x}{x!})^{\frac{1}{x}} = e$

Prove that $\frac{(n+1)!}{(n-1)!}=n(n+1)$

How can I test the convergence of the following sequence with odd products over even ones?

Minimize $x$ in factorial division

Upper Bound on ${n \choose r} $

Is there a geometrical interpretation of this equality $2\cdot 4\cdot 6\cdot\ldots\cdot(2n)=2^nn!$?

Limit of the spherical Bessel function of the second kind

Does it make sense to multiply probabilities?

Factorials and equivalency

What is $\int\limits_{0}^{1} \left[x(1-x)\right]^m \, dx$ ($m$ positive integer)?

How to prove this gamma identity?

Help required to compute logic of an answer.

How to prove that $(p^2)!$ is divisible by $(p!)^{p+1}$?

Excluding interval from N

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