\( \sum_{r=1}^{n} \tan ^{-1}\left(\frac{2^{r-1}}{1+2^{2 r-1}}\right) \) is equal to
(a) \( \tan ...
\( \sum_{r=1}^{n} \tan ^{-1}\left(\frac{2^{r-1}}{1+2^{2 r-1}}\right) \) is equal to
(a) \( \tan ^{-1}\left(2^{\mathrm{n}}\right) \)
(b) \( \tan ^{-1}\left(2^{\mathrm{n}}\right)-\frac{\pi}{4} \)
(c) \( \tan ^{-1}\left(2^{n+1}\right) \)
(d) \( \tan ^{-1}\left(2^{n+1}\right)-\frac{\pi}{4} \)
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