If y = x - x^2 + x^3 - x^4 + dots infty,then | vedclass

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(D) Given the infinite geometric series: $y = x - x^2 + x^3 - x^4 + \dots \infty$ This is a geometric series with first term $a = x$ and common ratio

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

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(D) Given the infinite geometric series: $y = x - x^2 + x^3 - x^4 + \dots \infty$ This is a geometric series with first term $a = x$ and common ratio $r = -x$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$. Substituting the values: $y = \frac{x}{1 - (-x)} = \frac{x}{1 + x}$. Now,solve for $x$: $y(1 + x) = x$ $y + xy = x$ $y = x - xy$ $y = x(1 - y)$ $x = \frac{y}{1 - y}$

If $y = x - x^2 + x^3 - x^4 + \dots \infty$,then the value of $x$ is equal to:

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