Question

proving an equation involving factorials is impossible

score 35 · Answer 1 · 2026-04-11 04:15:17

35

Views

proving an equation involving factorials is impossible

Published on 11 Apr 2026 - 4:15

score 40 · Answer 2 · 2026-04-13 18:45:45

40

Views

How does $\frac{(2n)!}{(2(n+1))!}$ become $\frac{1}{2(n+1)(2n+1)}$?

Published on 13 Apr 2026 - 18:45

score 282 · Answer 3 · 2026-04-14 08:17:37

282

Views

Relation connecting $(3n)!$, $3^n$ and $n!$

Published on 14 Apr 2026 - 8:17

score 74 · Answer 4 · 2022-06-27 01:42:24

74

Views

Express $\frac{1}{2n + 1}\,,\,n\in\mathbb{N}$ as a series of the form $\sum_{m = 0}^\infty\frac{a_m n!}{(n + m)!}\,.$

Published on 27 Jun 2022 - 1:42

score 131 · Answer 5 · 2026-04-13 18:13:03

131

Views

How $5^{40} < 4^{60} < 27^{30}$, $8^{1/11} < 9^{1/10} < 10^{1/9}$, $e^{e} < \pi^{e} < e^{\pi}$, and $200^{100} < 200! < 100^{200}$?

Published on 13 Apr 2026 - 18:13

score 177 · Answer 6 · 2022-07-01 14:46:37

177

Views

Calculate $\lim \sqrt[n] \frac{(2n)!}{(n !)^2}.$

Published on 01 Jul 2022 - 14:46

score 50 · Answer 7 · 2022-07-03 18:34:58

50

Views

Indefinite integral of $\frac{(z+2 n-3)\text{!!}}{(z-2 n+1)\text{!!}}$

Published on 03 Jul 2022 - 18:34

score 85 · Answer 8 · 2026-04-10 14:51:17

85

Views

Simplifying binomial sum of factorials

Published on 10 Apr 2026 - 14:51

score 374 · Answer 9 · 2026-04-14 07:23:30

374

Views

How many simple substitution ciphers are there that leave no letter fixed

Published on 14 Apr 2026 - 7:23

score 65 · Answer 10 · 2022-07-08 20:11:43

65

Views

Evaluating $ \lim_{n \to \infty} {\sqrt[n]{\frac{(2n - 1)!}{n!}}} $

Published on 08 Jul 2022 - 20:11

score 40 · Answer 11 · 2026-03-25 20:15:23

40

Views

Reasoning about limits related to the prime number theorem

Published on 25 Mar 2026 - 20:15

score 115 · Answer 12 · 2026-04-13 19:45:59

115

Views

How would one go about summing the factorials?

Published on 13 Apr 2026 - 19:45

score 156 · Answer 13 · 2022-07-13 06:02:34

156

Views

Finding $n$ such that $\frac{n+1}{n}$ < $\frac{\sqrt[n+1]{(n+1)!}}{\sqrt[n]{n!}}$

Published on 13 Jul 2022 - 6:02

score 87 · Answer 14 · 2026-04-13 09:53:44

87

Views

Finite many primes for every positive integer $b$?

Published on 13 Apr 2026 - 9:53

score 79 · Answer 15 · 2026-03-30 08:01:45

79

Views

Closed form for $\Gamma(n+\frac{2}{3})$

Published on 30 Mar 2026 - 8:01

List Question

proving an equation involving factorials is impossible

How does $\frac{(2n)!}{(2(n+1))!}$ become $\frac{1}{2(n+1)(2n+1)}$?

Relation connecting $(3n)!$, $3^n$ and $n!$

Express $\frac{1}{2n + 1}\,,\,n\in\mathbb{N}$ as a series of the form $\sum_{m = 0}^\infty\frac{a_m n!}{(n + m)!}\,.$

How $5^{40} < 4^{60} < 27^{30}$, $8^{1/11} < 9^{1/10} < 10^{1/9}$, $e^{e} < \pi^{e} < e^{\pi}$, and $200^{100} < 200! < 100^{200}$?

Calculate $\lim \sqrt[n] \frac{(2n)!}{(n !)^2}.$

Indefinite integral of $\frac{(z+2 n-3)\text{!!}}{(z-2 n+1)\text{!!}}$

Simplifying binomial sum of factorials

How many simple substitution ciphers are there that leave no letter fixed

Evaluating $ \lim_{n \to \infty} {\sqrt[n]{\frac{(2n - 1)!}{n!}}} $

Reasoning about limits related to the prime number theorem

How would one go about summing the factorials?

Finding $n$ such that $\frac{n+1}{n}$ < $\frac{\sqrt[n+1]{(n+1)!}}{\sqrt[n]{n!}}$

Finite many primes for every positive integer $b$?

Closed form for $\Gamma(n+\frac{2}{3})$

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