Problem in Arithmetic Mean - Geometric Mean inequality
3030
Proving inequality $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+\frac{3\sqrt[3]{abc}}{a+b+c} \geq 4$
47644
Inequality involving rearrangement: $ \sum_{i=1}^n |x_i - y_{\sigma(i)}| \ge \sum_{i=1}^n |x_i - y_i|. $
15232
Proving an inequality involving real powers
139692
Proof of inequality using AM-GM inequality
59675
A inequality proposed at Zhautykov Olympiad 2008
135219
On the mean value of a multiplicative function: Prove that $\sum\limits_{n\leq x} \frac{n}{\phi(n)} =O(x) $
72113
Geometric mean never exceeds arithmetic mean
147785
Proving inequality $x^xy^y \geq (\frac{x+y}{2})^{x+y}$
139711
prove this inequality with $\sum\limits_\text{cyc}\sqrt{1-xy}\ge 2$
137522
Hard inequality $ (xy+yz+zx)\left(\frac{1}{(x+y)^2}+\frac{1}{(y+z)^2}+\frac{1}{(z+x)^2}\right)\ge\frac{9}{4} $
73771
An inequality for a sum of sine functions
4064
An equality involving the mean value property
70621
Question concerning the mean-value property
113956
Proof variance of Geometric Distribution
103947
Inequality : $\sum_{k=1}^n x_k\cdot \sum_{k=1}^n \frac{1}{x_k} \geq n^2$
106979
Prove the inequality and limitation
62462
Problem with inequality: $ \left| \sqrt{2}-\frac{p}{q} \right| > \frac{1}{3q^2}$