JEE Main 2026 · 5 Apr · Shift 1, Mathematics question 24

Each term.
$$\frac{2^{p-1}}{1+2^{2p-1}}=\frac{2^p-2^{p-1}}{1+2^p\cdot2^{p-1}},$$
so the term is $\tan^{-1}2^p-\tan^{-1}2^{p-1}$.

Telescoping. The sum is $\tan^{-1}2^{11}-\tan^{-1}1=\tan^{-1}2048-\tfrac\pi4$, so $\alpha=\tan^{-1}2048$.

Answer: $\tan\alpha=2048$