The value of is equal to:

MATHEMATICS · Single correct · ISC · Mathematics · Sets and Functions · Sets and Functions

Problem

The value of ∑r=1∞tan⁡−1(1r2+5r+7)\sum_{r=1}^{\infty}\tan^{-1}\left(\frac{1}{r^2+5r+7}\right) is equal to: (1) tan⁡−13\tan^{-1}3 (2) π4\frac{\pi}{4} (3) sin⁡−1110\sin^{-1}\frac{1}{\sqrt{10}} (4) cot⁡−12\cot^{-1}2

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