# If only it was (n-1)(n+1)

The Fibonacci sequence is given by $F_1 = 1$, $F_2 = 1$ and $F_{n+1} = F_n + F_{n-1}$. What is

$\sum_{n=2}^\infty \frac{ 1 } { F_{n-1} F_{n+1} } ?$