# Fibonacci Product

Algebra Level 5

Let $F_{n}$ be a Fibonacci number , that is , $F_{0} = 0 , F_{1} = 1 , F_{n} = F_{n - 1} + F_{n - 2}$ for $n \geq 3$

then $\displaystyle \prod_{ n =2}^{\infty} \Big(1 + \frac{2}{F_{2n} - 1}\Big) =$

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