# Calculus problem by Sutirtha Datta

Calculus Level pending

$\large \lim_{n \to \infty}\frac{1}{n} \sum_{k=0}^{n-1}\cos \left(\frac{k\pi}{2n} \right) = \frac a{b\pi}$

$$a$$ and $$b$$ are coprime positive integers satisfying the equation above. Find $$a+b$$.

Notation: $$\lfloor \cdot \rfloor$$ denotes the floor function.

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