# Infinitely many capacitors

Calculus Level 5

$\large \sum_{n=0}^\infty \left(\int_{r_n}^{r_{n+1}} f(x) \, dx \right)^{-1} = \dfrac1C$

Let $$r_n$$ denote the $$n^\text{th}$$ smallest non-negative root of $$f(x) = \sin\sqrt x$$, where $${r_0}=0$$. Find $$C$$.

If you believe that the sum above diverges, write your answer as zero.

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