# What is the sum of Fibonacci reciprocals?

How can I calculate $\sum\limits_{n=1}^{\infty}\frac{1}{F_n}$, where $F_0=0$, $F_1=1$ and $F_n=F_{n-1}+F_{n-2}$?

Empirically, the result is around $3.35988566$.

Is there a "more mathematical way" to express this?

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You should do something about the first term. As it is, your series starts with $\frac{1}{0}$. – Dan Shved Mar 30 '14 at 6:04
@Dan Shved: Yep, thanks! – barak manos Mar 30 '14 at 6:04