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The sum of series $\frac{x}{1 - x^{2}} + \frac{x^{2}}{1 - x^{4}} + \frac{x^{4}}{1 - x^{8}} + \dots$ to infinite terms, if $f | x | < 1 is$

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Correct option is B

We have,tn=x2n−11−x2n−1=1+x2n−1−11+x2n−11−x2n−1=11−x2n−1−11−x2nTherefore,Sn=∑n=1n tn=11−x−11−x2+11−x2−11−x4 +…+11−x2n−1−11−x2n =11−x−11−x2n

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The sum of series x1−x2+x21−x4+x41−x8+…to infinite terms, if f|x|<1 is

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The sum of series $\frac{x}{1 - x^{2}} + \frac{x^{2}}{1 - x^{4}} + \frac{x^{4}}{1 - x^{8}} + \dots$ to infinite terms, if $f | x | < 1 is$