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 \(n \ge 2\).


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