Question

If $n$ is any odd number, prove that $\displaystyle{\sum_{k=1}^{n-1}\frac{(n-1)!}{k} \equiv 0 \pmod{n}}$.

score 92 · Answer 1 · 2017-05-04 08:13:56

92

Views

If $n$ is any odd number, prove that $\displaystyle{\sum_{k=1}^{n-1}\frac{(n-1)!}{k} \equiv 0 \pmod{n}}$.

Published on 04 May 2017 - 8:13

score 490 · Answer 2 · 2017-05-05 10:19:18

490

Views

Is this differentiation of factorial valid?

Published on 05 May 2017 - 10:19

score 68 · Answer 3 · 2026-04-05 17:03:03

68

Views

Limit $\lim_{n\to \infty} \frac{(2n+3)!} {2^{n+2}\, (n+1)!\, (n+1)! }$

Published on 05 Apr 2026 - 17:03

score 156 · Answer 4 · 2026-02-24 07:06:04

156

Views

Comparing the Least Common Multiple for $n!$ to the square root of $n!$

Published on 24 Feb 2026 - 7:06

score 53 · Answer 5 · 2017-05-07 09:30:59

53

Views

Can be ∑P/k! be broken down in a expression without the sum?

Published on 07 May 2017 - 9:30

score 47 · Answer 6 · 2017-05-07 17:04:10

47

Views

Using differential calculus to prove a fact on exponents

Published on 07 May 2017 - 17:04

score 96 · Answer 7 · 2026-03-30 12:04:19

96

Views

Inequality proof regarding factorial

Published on 30 Mar 2026 - 12:04

score 61 · Answer 8 · 2017-05-08 20:49:04

61

Views

Factorial expression of $\frac{n!}{(n-r)!}$

Published on 08 May 2017 - 20:49

score 35 · Answer 9 · 2017-05-08 21:04:19

35

Views

Ratio test involving factorials: $a_{n} = \frac{n-2}{(n+1)!}$; finding $\lim_{n \to \infty} |\frac{a_{n+1}}{a_n}|$

Published on 08 May 2017 - 21:04

score 56 · Answer 10 · 2026-02-24 07:02:48

56

Views

Comparing the Least Common Multiple to a Binomial Coefficient

Published on 24 Feb 2026 - 7:02

score 54 · Answer 11 · 2017-05-09 17:21:46

54

Views

Calculate number of primes

Published on 09 May 2017 - 17:21

score 1.5k · Answer 12 · 2017-05-10 15:58:58

1.5k

Views

An integral formula for the reciprocal gamma function

Published on 10 May 2017 - 15:58

score 67 · Answer 13 · 2017-05-10 16:28:57

67

Views

how can (k+1)! (k+2)-1 be (k+2)!-1?

Published on 10 May 2017 - 16:28

score 41 · Answer 14 · 2017-05-12 04:05:10

41

Views

Proof for $\frac{1}{n}\ln\left[2\sum_{i=0}^{n-1}\binom{\alpha n-1}{i}\right]\leq \alpha \ln(\alpha)-(\alpha-1)\ln(\alpha-1)$

Published on 12 May 2017 - 4:05

score 339 · Answer 15 · 2017-05-12 16:14:36

339

Views

What is the path for solving $(20! \cdot 12!) \bmod 2012$?

Published on 12 May 2017 - 16:14

List Question

If $n$ is any odd number, prove that $\displaystyle{\sum_{k=1}^{n-1}\frac{(n-1)!}{k} \equiv 0 \pmod{n}}$.

Is this differentiation of factorial valid?

Limit $\lim_{n\to \infty} \frac{(2n+3)!} {2^{n+2}\, (n+1)!\, (n+1)! }$

Comparing the Least Common Multiple for $n!$ to the square root of $n!$

Can be ∑P/k! be broken down in a expression without the sum?

Using differential calculus to prove a fact on exponents

Inequality proof regarding factorial

Factorial expression of $\frac{n!}{(n-r)!}$

Ratio test involving factorials: $a_{n} = \frac{n-2}{(n+1)!}$; finding $\lim_{n \to \infty} |\frac{a_{n+1}}{a_n}|$

Comparing the Least Common Multiple to a Binomial Coefficient

Calculate number of primes

An integral formula for the reciprocal gamma function

how can (k+1)! (k+2)-1 be (k+2)!-1?

Proof for $\frac{1}{n}\ln\left[2\sum_{i=0}^{n-1}\binom{\alpha n-1}{i}\right]\leq \alpha \ln(\alpha)-(\alpha-1)\ln(\alpha-1)$

What is the path for solving $(20! \cdot 12!) \bmod 2012$?

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