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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