Is $\frac{(3n)!}{n!(n+1)!(n+2)!}$ integer for any integer $n \ge 3$?
5257
Proving that $(3n)!$ is divisible by $n! \times (n + 1)! \times (n + 2)!$ if $n$ is greater than 2
102334
How can you prove $\frac{n(n+1)(2n+1)}{6}+(n+1)^2= \frac{(n+1)(n+2)(2n+3)}{6}$ without much effort?
47827
Prove that $\sum^{n}_{r=0}(-1)^r\cdot \large\frac{\binom{n}{r}}{\binom{r+3}{r}} = \frac{3!}{2(n+3)}$
61466
what is $\int_{|z|=3}\frac{1}{(z-2)^n(z-4)^m}dz$ for $m,n\in\mathbb{N}$?
31911
Is $\sum_{n=1}^{\infty}\frac{(\log\log2)^n}{n!}>\frac{3}{5}$
56624
Prove that $0!+1! + 2! + 3! + ..... + n!$ $\neq$ $p^\text{r}$, where $n \geqslant 3$ and $n$, $p$ and $r$ are three integers
86413
Show that $\frac{(m+n-1)!}{m!n!}$ is an integer where m and n are positive integers and gcd(m,n)=1
120573
Does $a!b!$ always divide $(a+b)!$
27580
Use mathematical induction to prove $ (2n)!\geq 2^n(n!)^2$ for $n \in \mathbb{N}$
59006
Proof of $\gcd(n!+1, (n+1)!+1)=1$?
64336
Show $\sum_{k=1}^n \frac{1}{k^2} \le 2$ and $\ln(n!) \ge 1 -n+n\ln(n)$ for all positive integers n
145891
Prove that $n! > \sqrt{n^n}, n \geq 3$
96039
Why is $\frac {1\cdot2\cdot3\cdot...\cdot n}{(n+1)(n+2)...(2n)}\le \frac 1 {n+1}$
45914
Proving that $n!≤((n+1)/2)^n$ by induction
27147
Proving $n! > n^3$ for all $n > a$
14064
Proof by induction that $\sum_{i=1}^n \frac{i}{(i+1)!}=1- \frac{1}{(n+1)!}$
91105
For every $n\ge3$ there exists $n$ different integers $a_1,...,a_n$ so that $\frac{1}{a_1}+\frac{1}{a_2}+...+\frac{1}{a_n}=1$