Question

Prove that $\frac{(n!)!}{(n!)^{(n-1)!}} $ is always an integer.

score 230 · Answer 1 · 2016-08-09 10:11:49

230

Views

Prove that $\frac{(n!)!}{(n!)^{(n-1)!}} $ is always an integer.

Published on 09 Aug 2016 - 10:11

score 179 · Answer 2 · 2016-08-11 02:27:17

179

Views

Prove that $\frac{d}{dx} x!^{1/x}$ converges at $\frac1e$

Published on 11 Aug 2016 - 2:27

score 346 · Answer 3 · 2016-08-11 19:21:08

346

Views

Triangular numbers and Wilson's Theorem

Published on 11 Aug 2016 - 19:21

score 90 · Answer 4 · 2016-08-13 15:25:15

90

Views

How to quickly calculate large factorials by hand

Published on 13 Aug 2016 - 15:25

score 2.5k · Answer 5 · 2016-08-15 01:56:12

2.5k

Views

Prove nth root of n! is less than n+1 th root of ((n+1) !): $\sqrt[n]{n!}\lt \sqrt[n+1]{(n+1)!}$?

Published on 15 Aug 2016 - 1:56

score 221 · Answer 6 · 2026-03-25 10:59:03

221

Views

Is this observation equivalent to Legendre's conjecture? $\forall n \in \Bbb N^+, \exists k \in \Bbb N^+:\ \ (n^2)\# \lt k! \lt (n+1)^2\#$

Published on 25 Mar 2026 - 10:59

score 65 · Answer 7 · 2026-03-27 15:11:42

65

Views

Use combinations to explain why $C(n, k) = C(n, n-k)$ for any $n, k ∈ ℕ, 0 ≤ k ≤ n$.

Published on 27 Mar 2026 - 15:11

score 80 · Answer 8 · 2016-08-16 15:18:21

80

Views

Are there Infinity many natural numbers (that are not factorials) that divide all factorials (greater than that number) evenly?

Published on 16 Aug 2016 - 15:18

score 190 · Answer 9 · 2026-03-25 19:05:15

190

Views

Convergence of $\sum_{n=1}^\infty\frac{n}{(n+1)!}$

Published on 25 Mar 2026 - 19:05

score 890 · Answer 10 · 2016-08-19 16:08:42

890

Views

Finding the Total number of permutation using a selective formula

Published on 19 Aug 2016 - 16:08

score 305 · Answer 11 · 2016-08-19 23:17:25

305

Views

Correctness of Factorial $(\text{mod } p)$ procedure

Published on 19 Aug 2016 - 23:17

score 6.7k · Answer 12 · 2016-08-20 12:20:44

6.7k

Views

How many possible combination of atoms are there in the universe.

Published on 20 Aug 2016 - 12:20

score 135 · Answer 13 · 2016-08-21 07:58:59

135

Views

How to solve equations in the form $f(x) = x!$?

Published on 21 Aug 2016 - 7:58

score 1.2k · Answer 14 · 2026-03-28 06:23:30

1.2k

Views

Notation For Summation of Factorials

Published on 28 Mar 2026 - 6:23

score 9k · Answer 15 · 2016-08-22 10:28:06

9k

Views

Mathematical induction problem: $\frac12\cdot \frac34\cdots\frac{2n-1}{2n}<\frac1{\sqrt{2n}}$

Published on 22 Aug 2016 - 10:28

List Question

Prove that $\frac{(n!)!}{(n!)^{(n-1)!}} $ is always an integer.

Prove that $\frac{d}{dx} x!^{1/x}$ converges at $\frac1e$

Triangular numbers and Wilson's Theorem

How to quickly calculate large factorials by hand

Prove nth root of n! is less than n+1 th root of ((n+1) !): $\sqrt[n]{n!}\lt \sqrt[n+1]{(n+1)!}$?

Is this observation equivalent to Legendre's conjecture? $\forall n \in \Bbb N^+, \exists k \in \Bbb N^+:\ \ (n^2)\# \lt k! \lt (n+1)^2\#$

Use combinations to explain why $C(n, k) = C(n, n-k)$ for any $n, k ∈ ℕ, 0 ≤ k ≤ n$.

Are there Infinity many natural numbers (that are not factorials) that divide all factorials (greater than that number) evenly?

Convergence of $\sum_{n=1}^\infty\frac{n}{(n+1)!}$

Finding the Total number of permutation using a selective formula

Correctness of Factorial $(\text{mod } p)$ procedure

How many possible combination of atoms are there in the universe.

How to solve equations in the form $f(x) = x!$?

Notation For Summation of Factorials

Mathematical induction problem: $\frac12\cdot \frac34\cdots\frac{2n-1}{2n}<\frac1{\sqrt{2n}}$

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