A Fibonacci series

Calculus Level 3

Let $F_n$ be the $n$ th Fibonacci number, where $F_1=1$ , $F_2=1$ and $F_{n+1}=F_n+F_{n-1}$ , for $n \geq 2$ . Evaluate the sum $\sum_{n=2}^\infty \frac{F_n}{F_{n+1} F_{n-1}}.$