# Fibonacci Product

Calculus Level 5

$\large \prod_{n=2}^\infty \left(1-\dfrac{2}{F_{n+1}^2-F_{n-1}^2+1}\right)$

Let $$F_n$$ denote the $$n^\text{th}$$ Fibonacci number, $$F_0 = 0, F_1 = 1$$ and $$F_n = F_{n-1} + F_{n-2}$$ where $$n=2,3,4,\ldots$$.

If the product above is equal to $$\dfrac AB$$, where $$A$$ and $$B$$ are coprime positive integers, find $$A+B$$.

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