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

\(a\) 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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