Useful inequalities

Here is a list of useful inequalities:

Name	Inequality
Cauchy-Schwarz inequality	For $$a_1,...,a_n,b_1,...,b_n\in\mathbb{R}$$ we have $$\sum^n_{i=1}a_ib_i\le\sqrt{\sum^n_{k=1}a_i^2}\sqrt{\sum^n_{i=1}b_i^2}$$