real analysis - Show that $sum_{n=1}^infty (frac{1}{a_{n+1}} - frac{1}{a_n})$ converges

Let $(a_n)_n$ be a sequence, in which $a_n\geq 0$ for all $n\in\mathbb{N}$, and $\lim_{n\rightarrow\infty} a_n = \infty$. Show that $\sum_{n=1}^\infty (\frac{1}{a_{n+1}} - \frac{1}{a_n})$ converges.

I tried to use the Cauchy Criterion but couldn't conclude anything. Can someone help?