If \( |r|1 \), then sum of the series \( \frac{1}{1+x}+\frac{2}{1+x...

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If \( |r|1 \), then sum of the series \( \frac{1}{1+x}+\frac{2}{1+x^{2}}+\frac{2^{2}}{1+x^{4}} \)
P \( +\frac{2^{3}}{1+x^{8}}+\ldots \) upto \( \infty \) is \( \frac{1}{x-\lambda} \), then the value of \( \lambda \) is

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