Fibonacci Summation

Calculus Level 3

\[\large\sum_{n=2}^{\infty}\dfrac1{F_{n-1}F_{n+1}}\]

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 sum above.

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