Sum of infinite terms of the series is

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Sum of infinite terms of the series cot⁡−1(12+34)+cot⁡−1(22+34)+cot⁡−1(32+34)+…\cot^{-1}\left(1^2 + \frac{3}{4}\right) + \cot^{-1}\left(2^2 + \frac{3}{4}\right) + \cot^{-1}\left(3^2 + \frac{3}{4}\right) + \dots is (1) π/4\pi/4 (2) tan⁡−12\tan^{-1}2 (3) tan⁡−13\tan^{-1}3 (4) tan⁡−14\tan^{-1}4

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