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$\underset{n \to \infty}{L t} \sum_{r = 1}^{n} \frac{1}{\sqrt{4 n^{2} - r^{2}}}$

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detailed solution

Correct option is D

Ltn→∞⁡1n∑r=1n 14−rn2=∫01 14−x2dx=sin−1⁡x201=sin−1⁡12−sin−1⁡(0)=π6−0=π6

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Ltn→∞∑r=1n14n2−r2

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$\underset{n \to \infty}{L t} \sum_{r = 1}^{n} \frac{1}{\sqrt{4 n^{2} - r^{2}}}$