If $ |x| < 1 $ and $y=x-\large\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+......$ then x is equal to :

Question

\[\begin {array} {1 1} (a)\;y+\frac{y^2}{2}+\frac{y^3}{3}+.....\\(b)\;y-\frac{y^2}{2}+\frac{y^3}{3}-\frac{y^4}{4}..... \\ (c)\;y-\frac{y^2}{2!}+\frac{y^3}{3!}+.....\\ (d)\;y-\frac{y^2}{2!}+\frac{y^3}{3!}-\frac{y^4}{4!}.....\end {array}\]