The value of is

MATHEMATICS · Single correct · AoPS · Mathematics · Sequences & Series · Sequences & Series

Problem

The value of

\sum_{r=2}^{\infty}\tan^{-1}\left(\frac{1}{r^2-5r+7}\right)

is (1)

\frac{\pi}{4}

(2)

\frac{\pi}{2}

(3)

\frac{3\pi}{4}

(4)

\frac{5\pi}{4}