Telescoping series

Let $(a_n{)}_{n=0}^{\mathrm{\infty }}$ be a sequence of real numbers which converge to 0, i.e., $li{m}_{n\to \mathrm{\infty }}{a}_n=0$. Then the series $\sum _{n=0}^{\mathrm{\infty }}(a_n-a_{n+1})$ converges to $a_0$.