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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