Question

If x is equal to one + y + y square + upto infinity why is less than one then find the value of y in terms of x

Answer 1

$x = 1 + y + {y}^{2} ....... \infty \\ it \: is \: in \: gp \\ using \: formula \: of \: infinite \: sum \\ sum = \frac{a}{1 - r} \\ = \frac{1}{1 - y} = x \\ \frac{1}{x} = 1 - y \\ y = 1 - \frac{1}{x} \\ y = \frac{x - 1}{x}$