Question

$\cot^{-1}(2 \cdot 1^2) + \cot^{-1}(2 \cdot 2^2) + \cot^{-1}(2 \cdot 3^2) + \dots \dots \infty =$

• A. $\frac{\pi}{2}$
• B. $\frac{\pi}{3}$
• C. $\frac{\pi}{4}$
• D. $\frac{\pi}{8}$

Hint:

To sum $\tan^{-1}$ series, express the argument as $\frac{x-y}{1+xy}$ to create a telescoping sum.

Answer 1

The Correct Option is C