JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

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Analyzing +4 | -1

The sum of the series

\frac{1}{{x + 1}} + \frac{2}{{{x^2} + 1}} + \frac{{{2^2}}}{{{x^4} + 1}} + .... + \frac{{{2^{100}}}}{{{x^{{2^{100}}}} + 1}}\,

, when

x = 2

View answer and explanation

Correct option: D

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

The correct answer is D (

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

) because it is the result of telescoping the series and substituting x = 2.

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