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

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(D) The given series is an infinite geometric series: $y = x - x^2 + x^3 - x^4 + \dots \infty$.This is a geometric progression with the first term $a

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

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

If $y = x - x^2 + x^3 - x^4 + \dots \infty$,then the value of $x$ will be

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