If $< 1$ then $\frac{1 - 2 x}{1 - x x^{2}} + \frac{2 x - 4 x^{3}}{1 - x^{2} + x^{4}} + \frac{4 x^{3} - 8 x^{7}}{10 x^{4} + x^{8}} + \dots \infty =$

A

$\frac{1 + 2 x}{1 + 1 + x^{2}}$

B

$\frac{1 - 2 x}{1 + x + x^{2}}$

C

$\frac{{(1 + 2 x)}^{2}}{1 + x + x^{2}}$

D

$\frac{{(1 + 2 x)}^{3}}{1 + x + x^{2}}$

Text Solution

Verified by Experts

The correct Answer is:A

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Updated on:21/07/2023

Class 12 MATHS DIFFERENTIATION

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Question 1 - Select One or More
If $x = \frac{1}{2}$ and if $\frac{1 - 2 x}{1 - x + x^{2}} + \frac{2 x - 4 x^{3}}{1 - x^{2} + x^{4}} + \frac{4 x^{3} - 8 x^{7}}{1 - x^{4} + x^{6}} + ... \infty = k$ , then
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If $x = \frac{1}{2}$ then $\frac{1 - 2 x}{1 - x + x^{2}} + \frac{2 x - 4 x^{3}}{1 - x + x^{4}} + \frac{4 x^{3} - 8 x^{7}}{1 - x^{4} + x^{6}} + ... . . \infty$ is
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