Show that $\lim_{n\rightarrow \infty}\frac{a_1+a_2+\ldots +a_n}{n}=0 \iff \lim_{n\rightarrow \infty} \frac{a_{1}^2+a_{2}^2+\ldots +a_{n}^2}{n}=0$
Sequence such that $\lim\limits_{n\to \infty} \frac{x_1^2+x_2^2+...+x_n^2}{n}=0$