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Simplify $\sum\limits_{k = 0}^n {{2^k}\tan ({2^k}x)}$ which $k \in \{ 0,1,...,n + 1\} ,{2^k}x \notin \{ 0,\frac{\pi }{2}\}$

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    P.S.: What does segma mean? I'm sure you didn't mean [this](http://www.urbandictionary.com/define.php?term=segma). But beware of inuendos. ;P2011-03-02

1 Answers 1

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Hint: $\ln(\cos(x))'=\tan(x)$ and Recursion.

Alternative route: Use the identity $\cot(x) - 2\cot(2x)=\tan(x)$ and telescoping.