# Not-So-Dumb Fibonacci Sum #1

Find the value of $\sum_{n=1}^{\infty} \dfrac{F_{n+1}}{F_{n}F_{n+2}}$

where $$F_n$$ is the $$n$$th Fibonacci number, defined by the recurrence relation $$F_n=F_{n-1}+F_{n-2}$$ with $$F_1=F_2=1$$.

×