Mathematics

Problem

The value of

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

is a.

1 + \sqrt{5}

-1 + \sqrt{5}

-1 + \sqrt{2}

1 + \sqrt{2}