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Prove that sum(r=1)^(n) tan^(-1) ((2^(r...

Prove that `sum_(r=1)^(n) tan^(-1) ((2^(r -1))/(1 + 2^(2r -1))) = tan^(-1) (2^(n)) - (pi)/(4)`

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To prove that \[ \sum_{r=1}^{n} \tan^{-1} \left( \frac{2^{r-1}}{1 + 2^{2r-1}} \right) = \tan^{-1} (2^n) - \frac{\pi}{4}, \] we will follow these steps: ...
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