Prove the following inequality using ${AM \geq GM}$
2554
Show that if $n>2$, then $(n!)^2>n^n$.
11983
Proof of Clarkson's Inequality
104807
Prove the inequality $\left|\frac{m}{n}-\frac{1+\sqrt{5}}{2}\right|<\frac{1}{mn}$
56101
Prove the inequality $\frac{a}{c+a-b}+\frac{b}{a+b-c}+\frac{c}{b+c-a}\ge{3}$
2455
Prove that $\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2$
122127
An "AGM-GAM" inequality
138819
Prove that $\phi(n) \geq \sqrt{n}/2$
52618
AM-GM inequality basic
149700
Prove that $\frac{a_1^2}{a_1+a_2}+\frac{a_2^2}{a_2+a_3}+ \cdots \frac{a_n^2}{a_n+a_1} \geq \frac12$
20863
how do I prove this inequallity?
86209
Show this inequality $\frac{n}{a_1 - a_0} + \frac{n - 1}{a_2 - a_1} + \cdots + \frac{1}{a_n - a_{n-1}} \ge \sum_{k=1}^n \frac{k^2}{a_k}$
110798
Problem using the AM-GM inequality
82591
Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
98454
Prove that, $\frac{a}{b}+\frac{b}{c}+\frac{c}{d}+\frac{d}{a}\ge 4$ where we do not use AM-GM inequality on the given statement to prove it.
116387
How to prove that $\Gamma(x) \leq x^x$ for $x \geq 1$
117680
Prove that $|e^{i\theta_1}-e^{i\theta_2}| \leq |\theta_1 - \theta_2|$
143968
Proving this inequality by mathematical induction