Prove inequality $(a_1+a_2+...+a_n)(\frac1{a_1}+\frac1{a_2}+...+\frac1{a_n})\geq n^2$ when $a_1,a_2,...,a_n$ are positive numbers.
Prove that $\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2$