Evaluate \[ \sum_{k=0}^{n} 2^k \tan \frac{\pi}{4\cdot 2^{n-k}}.\]

**GD Star Rating**

*loading...*

Evaluate \[ \sum_{k=0}^{n} 2^k \tan \frac{\pi}{4\cdot 2^{n-k}}.\]

Let \(m\) and \(n\) be odd integers. Determine \[ \sum_{k=1}^\infty \frac{1}{k^2}\tan\frac{k\pi}{m}\tan \frac{k\pi}{n}.\]

Compute tan^{-1}(1) -tan^{-1}(1/3) + tan^{-1}(1/5) – tan^{-1}(1/7) + … .