If |x|<1,y=x−x2+x3−x4+⋯⋯∞, then the value of x in terms of y is

|x|<1y=x−x2+x3−x4+⋯⋯∞y=x1+x (r=−x)x=y+xyx−xy=yx(1−y)=yx=y1−y

If |x|<1,y=x−x2+x3−x4+⋯⋯∞, then the value of x in terms of y is

|x|<1y=x−x2+x3−x4+⋯⋯∞y=x1+x (r=−x)x=y+xyx−xy=yx(1−y)=yx=y1−y

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If $| x | < 1, y = x - x^{2} + x^{3} - x^{4} + \dots \dots \infty$ , then the value of $x$ in terms of $y$ is

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$\frac{y}{y + 1}$

$\frac{1 - y}{y}$

$\frac{y}{y - 1}$

$\frac{y}{1 - y}$

answer is C.

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Detailed Solution

$| x | < 1$

$y = x - x^{2} + x^{3} - x^{4} + \dots \dots \infty$

$y = \frac{x}{1 + x} (r = - x)$

$x = y + x y$

$x - x y = y$

$x (1 - y) = y$

$x = \frac{y}{1 - y}$

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If |x|<1,y=x−x2+x3−x4+⋯⋯∞, then the value of x in terms of y is

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If $| x | < 1, y = x - x^{2} + x^{3} - x^{4} + \dots \dots \infty$ , then the value of $x$ in terms of $y$ is