# If Only It Was (n-2)(n+2)

The Fibonacci sequence is given by $$F_1 = 1$$, $$F_2 = 1$$, and $$F_{n+1} = F_n + F_{n-1}$$. What is $\sum_{n=3}^\infty \frac{ 1 } { F_{n-2} F_{n+2} } ?$ If your answer can be expressed as $$\frac{a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers, find $$a+b$$.

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