# Fibonacci Product

Algebra Level 5

$\large \prod_{n=2}^\infty \left(1 + \dfrac2{F_{2n} - 1} \right)$

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

Compute the infinite product above.

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