## Problem 2

Consider the sequence $\left(x_{n}\right) \mathrm{n} \geq 1$ of positive real numbers with $\lim _{n \rightarrow \infty} \mathrm{x}_{\mathrm{n}}=0$.

Calculate:

$\lim _{n \rightarrow \infty} \frac{\sqrt{x_{1}^{2}-x_{1} x_{2}+x_{2}^{2}}+\sqrt{x_{2}^{2}-x_{2} x_{3}+x_{3}^{2}}+\cdots+\sqrt{x_{n}^{2}-x_{n} x_{1}+x_{1}^{2}}}{n}$

GMB 4/2012