If `|x|gt1`,then sum of the series `(1)/(1+x)+(2)/(1+x^(2))+(2^(2))/(1+x^(4))+(2^(3))/(1+x^(8))+"......"" upto terms "oo` is `(1)/(x-lambda)`,then the value of `lambda` is

Explanation

To solve the problem, we need to find the value of \( \lambda \) given the series:

\[ S = \frac{1}{1+x} + \frac{2}{1+x^2} + \frac{2^2}{1+x^4} + \frac{2^3}{1+x^8} + \cdots \]

We know that this series converges to \( \frac{1}{x - \lambda} \).

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