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Q. $\displaystyle \lim_{n \to\infty} \frac{1}{n} \sum^{2n}_{r=1} \frac{r}{\sqrt{n^{2}+r^{2}} } $ equals

IIT JEEIIT JEE 1997Limits and Derivatives

Solution:

Correct answer is (b) $ - 1 +\sqrt{5}$