Prove that$ \frac{(n^2)!}{(n!)^n} \in$ Z
45645
Using permutation or otherwise, prove that $\frac{(n^2)!}{(n!)^n}$ is an integer,where $n$ is a positive integer.
20964
Proof that $n^2 < 2^n$
39073
Proving that: $\forall n \in \mathbb{N} :|f^{(n)}(x)|\leq \frac{1}{n+1}$
54369
Proof of $n^2 \leq 2^n$.
87813
How to show that for all k, $k! \ge (k/2)^{k/2}$
12020
Prove $\sqrt{n+1}-\sqrt{n}\lt \frac{1}{2\sqrt{n}}$
30495
Analysis: Prove divergence of sequence $(n!)^{\frac2n}$
78538
prove $\lim_{n\to\infty}{\frac{a^n}{n!}}=0$
137640
Proof that $\sum_{1}^{\infty} \frac{1}{n^2} <2$
26316
Convergence of $a_n= \frac{n!}{n^n}$?
72600
Proof that $n!\leq {(\frac{n+1}{2})}^{n}$
138905
Find the limit of $\log\Big(\frac{(n^2+n)!}{n^2!n^{2n}}\Big)$
98946
Prove that $(mn)!$ is divisible by $(n!)\cdot(m!)^n$
117863
Series $\sum_{n=1}^\infty \frac{n^n}{(n!)^2}$
34374
Simplifying factorials: $\frac{(n-1)!}{(n-2)!}$
132431
Proving $|f'(z)|\leq\frac{\text{Re}(f(z))}{\text{Re}(z)}$
35611
How can I show that $n! \leqslant \left(\frac{n+1}{2}\right)^n$?