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Calculus Level 3

\[ \large \lim_{n\to\infty} \frac1n \sum_{k=1}^n \cos\left(\frac{k\pi}{2n}\right) \]

If the limit above equals to \(A \pi^B\) for integers \(A\) and \(B\), find the value of \(A\times B\).

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