Question

Show that $V_n^k=\frac{n!}{(n-k)!}$

score 31 · Answer 1 · 2021-04-24 17:49:17

31

Views

Show that $V_n^k=\frac{n!}{(n-k)!}$

Published on 24 Apr 2021 - 17:49

score 106 · Answer 2 · 2026-04-03 21:01:04

106

Views

Inverse to Stirling's Approximation

Published on 03 Apr 2026 - 21:01

score 49 · Answer 3 · 2026-04-12 04:18:14

49

Views

How to calculate the right-most digits of $\lim_{n\to\infty}\sum_{k=0}^n k!$

Published on 12 Apr 2026 - 4:18

score 96 · Answer 4 · 2021-04-27 14:47:04

96

Views

Showing $(n)^{\overline{k}}=(n+k-1)^{\underline{k}}=(-1)^k\cdot(-n)^{\underline{k}}$, for rising and falling factorials

Published on 27 Apr 2021 - 14:47

score 1.9k · Answer 5 · 2026-04-12 04:45:10

1.9k

Views

Proving $\Gamma(x)\Gamma(1-x)=\frac{\pi}{\sin(\pi x)}$

Published on 12 Apr 2026 - 4:45

score 131 · Answer 6 · 2026-04-12 04:45:07

131

Views

Is there a name for a factorial-like falling product which uses an arbitrary step $x \in \mathbb{R}$ instead of 1.

Published on 12 Apr 2026 - 4:45

score 500 · Answer 7 · 2026-04-11 05:58:55

500

Views

How to find the limit that involves the factorials?

Published on 11 Apr 2026 - 5:58

score 72 · Answer 8 · 2026-04-05 17:36:16

72

Views

Showing $(n+m)^{\underline{k}}=\sum_{v=0}^\infty{k\choose v}\cdot{(m)^{\underline{k-v}}}\cdot(n)^{\underline{v}}$ for falling factorials

Published on 05 Apr 2026 - 17:36

score 161 · Answer 9 · 2021-05-02 13:28:35

161

Views

Given $n$ is a positive integer less than $k$, how many values can $n$ take if $(n \pm x)$ is a factor of $n!$ where $x,k$ are also positive integers?

Published on 02 May 2021 - 13:28

score 787 · Answer 10 · 2026-04-06 08:07:28

787

Views

Type 1 Error Poisson Distribution

Published on 06 Apr 2026 - 8:07

score 77 · Answer 11 · 2026-04-11 15:41:53

77

Views

Junk Mail Permutations

Published on 11 Apr 2026 - 15:41

score 99 · Answer 12 · 2026-04-12 11:15:54

99

Views

Confusion about factorial $\dfrac{(N!)^2}{(2N)!}$

Published on 12 Apr 2026 - 11:15

score 1.5k · Answer 13 · 2021-05-03 17:26:31

1.5k

Views

When $40!$ is expressed in base $8$ form, what is the last non–zero digit in the base $8$ expansion?

Published on 03 May 2021 - 17:26

score 86 · Answer 14 · 2021-05-04 08:17:18

86

Views

Showing convergence of integral sequence

Published on 04 May 2021 - 8:17

score 66 · Answer 15 · 2026-04-08 10:52:14

66

Views

$b_n=\frac{(-n)^{n-1}}{n!}$ recursive form proof

Published on 08 Apr 2026 - 10:52

List Question

Show that $V_n^k=\frac{n!}{(n-k)!}$

Inverse to Stirling's Approximation

How to calculate the right-most digits of $\lim_{n\to\infty}\sum_{k=0}^n k!$

Showing $(n)^{\overline{k}}=(n+k-1)^{\underline{k}}=(-1)^k\cdot(-n)^{\underline{k}}$, for rising and falling factorials

Proving $\Gamma(x)\Gamma(1-x)=\frac{\pi}{\sin(\pi x)}$

Is there a name for a factorial-like falling product which uses an arbitrary step $x \in \mathbb{R}$ instead of 1.

How to find the limit that involves the factorials?

Showing $(n+m)^{\underline{k}}=\sum_{v=0}^\infty{k\choose v}\cdot{(m)^{\underline{k-v}}}\cdot(n)^{\underline{v}}$ for falling factorials

Given $n$ is a positive integer less than $k$, how many values can $n$ take if $(n \pm x)$ is a factor of $n!$ where $x,k$ are also positive integers?

Type 1 Error Poisson Distribution

Junk Mail Permutations

Confusion about factorial $\dfrac{(N!)^2}{(2N)!}$

When $40!$ is expressed in base $8$ form, what is the last non–zero digit in the base $8$ expansion?

Showing convergence of integral sequence

$b_n=\frac{(-n)^{n-1}}{n!}$ recursive form proof

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