# Summing up the reciprocals of Fibonacci numbers

Calculus Level 5

$\large \sum_{j=1}^{\infty} {\left( F_j \right)}^{-1} \ = \ ?$

$$\$$

Notation: $$F_n$$ denotes the $$n^{\text{th}}$$ Fibonacci number. A Fibonacci number is a number of the sequence generated by $$F_0 = 0$$, $$F_1 = 1$$ and $$F_n = F_{n-1} + F_{n-2}$$ for $$n \ge 2$$.