Question:medium

If \( \alpha = \frac{\pi}{4} + \sum_{p=1}^{11} \tan^{-1} \left( \frac{2^{p-1}}{1 + 2^{2p-1}} \right) \), then the value of \( \tan(\alpha) \) is:

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In \( \tan^{-1} \) summations, always try to split the numerator into a difference of two factors whose product (plus 1) matches the denominator.

Updated On: Apr 6, 2026

\( 2^9 \)
\( 2^{10} \)
\( 2^{11} \)
\( 2^{12} \)

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The Correct Option is C

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