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$lim_{n \to \infty} \frac{1}{n} \sum_{r = 1}^{2 n} \frac{r}{\sqrt{n^{2} + r^{2}}}$ equals

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Correct option is B

Required limit = limn→∞ 1n∑r=12n r/n1+r2/n2=∫02 x1+x2dx=1+x202=5−1.

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limn→∞ 1n∑r=12n rn2+r2 equals

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$lim_{n \to \infty} \frac{1}{n} \sum_{r = 1}^{2 n} \frac{r}{\sqrt{n^{2} + r^{2}}}$ equals