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