# Madhava from Sangamagrama?

Calculus Level 5

Let $$\{F_n\}$$ to be the Fibonacci's sequence, where $$F_1 = F_2=1$$ and $$F_{n + 1} = F_n + F_{n - 1}, \space \forall \, n \ge 2$$, and $\displaystyle \sum_{n = 1}^\infty \arctan \left(\frac{1}{F_{2n + 1}}\right) = \frac{A\pi}{B},$ where $$A$$ and $$B$$ are coprime positive integers. Find $$10A + B$$.

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