A) \[1+\sqrt{5}\]
B) \[-1+\sqrt{5}\]
C) \[-1+\sqrt{2}\]
D) \[1+\sqrt{2}\]
Correct Answer: B
Solution :
\[L=\underset{n\to \infty }{\mathop{\lim }}\,\,\,\sum\limits_{r=1}^{2n}{{}}\frac{1}{n}\,.\,\frac{r/n}{\sqrt{1+{{(r/n)}^{2}}}}\]=\[\int_{0}^{2}{{}}\frac{x}{\sqrt{1+{{x}^{2}}}}\,dx=\sqrt{5}-1\].
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