How can I prove by induction that $n!>n^{\frac n2}$ for $n>2$?
2554
Show that if $n>2$, then $(n!)^2>n^n$.
27304
Proving $ 1+\frac{1}{4}+\frac{1}{9}+\cdots+\frac{1}{n^2}\leq 2-\frac{1}{n}$ for all $n\geq 2$ by induction
153123
Proving by induction $4^n  0$
112907
Math Induction Proof: $(1+\frac1n)^n < n$
68480
Proof by Induction: Prove that $2^n > n^2$, for all natural numbers greater than or equal to $5$
114212
How to use Mathematical Induction to prove $\frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} + \cdots + \frac{1}{n(n + 1)} = \frac{n}{n + 1}$?
45645
Using permutation or otherwise, prove that $\frac{(n^2)!}{(n!)^n}$ is an integer,where $n$ is a positive integer.
121544
Proof by Induction: $2(\sqrt{n+1} - \sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n}-\sqrt{n-1})$
2197
Induction principle for $n!<n^n$
14435
Show by induction: $(1+\frac{1}{n})^{n}<n$
27147
Proving $n! > n^3$ for all $n > a$
100558
Prove that for any even positive integer $n$, $n^2-1 \mid 2^{n!}-1$
73002
For $n \geq 2$, prove that $(1- \frac{1}{4})(1- \frac{1}{9})(1- \frac{1}{16})...(1- \frac{1}{n^2}) = \frac{n+1}{2n}$
130093
Prove by Induction : $n < 2^n$
91197
Proving $n! \ge 2^{n-1 }$for all $n\ge1 $by mathematical Induction
44906
Use induction to prove that $2^n$ divides $(2n)!$ for any $n\in\mathbb{Z}_{\geq0}.$
18301
Proof by Induction involving Inequality and Factorials as denominators