Find-the-sum-to-infinite-terms-of-the-series-x-1-x-2-x-2-1-x-4-x-4-1-x-8-

Question Number 24438 by Tinkutara last updated on 18/Nov/17

Find the sum to infinite terms of the

series \frac{x}{1 - x^{2}} + \frac{x^{2}}{1 - x^{4}} + \frac{x^{4}}{1 - x^{8}} + \dots \dots

Commented by prakash jain last updated on 18/Nov/17

S = \frac{x}{1 - x^{2}} + \frac{x^{2}}{1 - x^{4}} + \frac{x^{4}}{1 - x^{8}} + \dots .

\frac{x}{1 - x^{2}} + \frac{x^{2}}{1 - x^{4}} = \frac{x + x^{2} + x^{3}}{1 - x^{4}}

\frac{x + x^{2} + x^{3}}{1 - x^{4}} + \frac{x^{4}}{1 - x^{8}} = \frac{x + x^{2} + x^{3} + x^{4} + x^{5} + x^{6} + x^{7}}{1 - x^{8}}

a s s u m i n g ∣ x ∣< 1

\Rightarrow S = \frac{x}{1 - x}

Commented by Tinkutara last updated on 18/Nov/17

Thank you very much Sir!