Mathematics

Mathematics

Problem

Evaluate lim⁡n→∞1n[sin⁡2kπ2n+sin⁡2k2π2n+⋯+sin⁡2kπ2]\lim_{n \to \infty} \frac{1}{n} \left[ \sin^{2k} \frac{\pi}{2n} + \sin^{2k} \frac{2\pi}{2n} + \dots + \sin^{2k} \frac{\pi}{2} \right]

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