# Fibonacci series

Calculus Level 5

$\large \sum_{n=0}^\infty \frac{1}{F_{2n+1}+1}=\frac{\sqrt{A}}{B}$

Let $$F_n$$ denote the $$n^\text{th}$$ Fibonacci number, where $$F_0 = 0, F_1 = 1$$ and $$F_n = F_{n-1} + F_{n-2}$$ for $$n=2,3,4,\ldots$$.

If the equation above holds true for positive integers $$A$$ and $$B$$, with $$A$$ square-free, find $$A+B$$.

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