Given average of positive bounded sequence converges to zero, does the average of the square sequence also converge?

Question

Given $\frac{\sum\limits_{i=1}^n |x_i|}{n}\rightarrow 0, |x_i|\leq C $, does $\frac{\sum\limits_{i=1}^n |x_i|^2}{n}\rightarrow 0$ also hold true?

Answer 1

Hint: $$\frac{\sum\limits_{i=1}^n |x_i|^2}{n}\leq C\frac{\sum\limits_{i=1}^n |x_i|}{n}$$