question_answer

\[\underset{n\to \infty }{\mathop{\lim }}\,\frac{1}{n}\underset{r=1}{\overset{2n}{\mathop{\sum }}}\,\frac{r}{\sqrt{{{n}^{2}}+{{r}^{2}}}}\] equals:

A)  \[1+\sqrt{5}\]              

B)  \[-1+\sqrt{5}\]

C)  \[-1+\sqrt{2}\]             

D)  \[1+\sqrt{2}\]

E)  None of these