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(A) The given series is an infinite geometric progression $(G.P.)$ with the first term $a = x$ and common ratio $r = x$.For an infinite $G.P.$ to conv

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

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(A) The given series is an infinite geometric progression $(G.P.)$ with the first term $a = x$ and common ratio $r = x$.For an infinite $G.P.$ to converge,$|r| The sum of an infinite $G.P.$ is given by the formula $S = \frac{a}{1 - r}$.Substituting the values,we get $y = \frac{x}{1 - x}$.Now,solve for $x$:$y(1 - x) = x$$y - yx = x$$y = x + yx$$y = x(1 + y)$$x = \frac{y}{1 + y}$.

If $y = x + x^2 + x^3 + \dots \infty$,then $x = $

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