\( \sum_{r=1}^{n} \tan ^{-1}\left(\frac{2^{r-1}}{1+2^{2 r-1}}\right) \) is equal to:....

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\( \sum_{r=1}^{n} \tan ^{-1}\left(\frac{2^{r-1}}{1+2^{2 r-1}}\right) \) is equal to:
\( \mathrm{P} \)
(A) \( \tan ^{-1}\left(2^{n}\right) \)
(B) \( \tan ^{-1}\left(2^{n}\right)-\frac{\pi}{4} \)
(C) \( \tan ^{-1}\left(2^{n+1}\right) \)
(D) \( \tan ^{-1}\left(2^{n+1}\right)-\frac{\pi}{4} \)


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