Fibonacci, inverted

Let \(F_n\) be the \(n\)th Fibonacci number, where \(F_1 = F_2 = 1.\) Also, let \[S = \sum_{n=1}^{\infty} \frac{1}{F_n}.\] Use a program to find \(\lfloor 10000\times S\rfloor .\)
Note: \(F_n\) is defined so that \(F_n = F_{n-1} + F_{n-2},\ n \in \mathbb{Z}.\)
Also note: \(\lfloor x \rfloor\) is defined as the greatest integer less than or equal to \(x.\)

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