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$\lim_{n \to \infty} \left(\frac{n}{n^2+1^2} + \frac{n}{n^2+2^2} + \frac{n}{n^2+3^2} + \cdots + \frac{1}{5n}\right)$ is equal to:
(1) $\frac{\pi}{4}$
(2) $\tan^{-1}(3)$
(3) $\frac{\pi}{2}$
(4) $\tan^{-1}(2)$
$= \lim_{n\to\infty}\sum_{r=0}^{2n}\frac{n}{n^2+r^2} = \int_0^2 \frac{dx}{1+x^2} = \left[\tan^{-1}x\right]_0^2 = \tan^{-1}2$.
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