JEE Mains · Maths · STD 11 - 8. sequence and series
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 :
- A \(1+\frac{2^{101}}{4^{101}-1}\)
- B \(1+\frac{2^{100}}{4^{101}-1}\)
- C \(1-\frac{2^{100}}{4^{100}-1}\)
- D \(1-\frac{2^{101}}{4^{101}-1}\)
Answer & Solution
Correct Answer
(D) \(1-\frac{2^{101}}{4^{101}-1}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{S}=\frac{1}{\mathrm{x}+1}+\frac{2}{\mathrm{x}^{2}+1}+\frac{2^{2}}{\mathrm{x}^{4}+1}+\ldots \frac{2^{100}}{\mathrm{x}^{2^{100}}+1}\)…
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