Prove that $(n!)^ 2 \gt n^n$
2554
Show that if $n>2$, then $(n!)^2>n^n$.
62177
Prove that: $2^n < n!$ Using Induction
52115
Show that $e^x > 1 + x + x^2/2! + \cdots + x^k/k!$ for $n \geq 0$, $x > 0$ by induction
2455
Prove that $\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2$
91197
Proving $n! \ge 2^{n-1 }$for all $n\ge1 $by mathematical Induction
99052
Prove that $( 1 + n^{-2}) ^n \to 1$.
133017
Prove that $n^n>1\times3\times5\times7\times \dots\times(2n-1)$
10629
How to prove $4(n!)>2^{n+2}$ for $ n\geq 4$ with induction
24403
Prove that $ n < 2^{n}$ for all natural numbers $n$.
79847
proving of inequality $(n!)^2 \leq n^n\cdot n!\leq (2n!)$, where $n\in \mathbb{N}$
44906
Use induction to prove that $2^n$ divides $(2n)!$ for any $n\in\mathbb{Z}_{\geq0}.$
19804
How to prove that $|w_{n+1}-w_n| \leq (2/3)^2 |w_n - w_{n-1}|$?
36436
Proving $\sum_{k=1}^n k k!=(n+1)!-1$
88055
Use induction to prove the following: $1! + 2! + .... + n! \le (n + 1)!$
9920
$(n^2 - 1)!$ is a multiple of $(n!)^n$
88838
How can I prove this inequality for $n\geq 2$?
145891
Prove that $n! > \sqrt{n^n}, n \geq 3$