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Question 56

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If lim⁡n→∞∑k=1nsin⁡(k/n2)=sin⁡θ\displaystyle\lim_{n\to\infty}\sum_{k=1}^n\sin(k/n^2)=\sin\theta for −π/2≤θ≤π/2-\pi/2\le\theta\le\pi/2, find θ\theta.

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