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The sum of the series \(\frac{1}{x+1}+\frac{2}{x^2+1}+\frac{2^2}{x^4+1}+\ldots+\frac{2^{100}}{x^{2^{100}}+1}\) when \(x=…

Q1

The sum of the series \(\frac{1}{x+1}+\frac{2}{x^2+1}+\frac{2^2}{x^4+1}+\ldots+\frac{2^{100}}{x^{2^{100}}+1}\) when \(x=2\) is:

[JEE Main 2021, 26 Aug (Shift 1)]

a

\(1-\frac{{2}^{100}}{{4}^{100}-1}\)

b

\(1-\frac{{2}^{101}}{{4}^{101}-1}\)

c

\(1+\frac{{2}^{100}}{{4}^{101}-1}\)

d

\(1+\frac{{2}^{101}}{{4}^{101}-1}\)

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