The value of is

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

The value of

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

is (1)

1 + \sqrt{5}

(2)

-1 + \sqrt{5}

(3)

-1 + \sqrt{2}

(4)

1 + \sqrt{2}