Express $1(1$ x$)2$ as a power series by differentiating the equation below. What is the radius of convergence?$11$ x $=1$ x x$2$ x$3=$ xnn $=0|$x$|<1$SolutionDifferentiating each side of the equation, we get the following$\mathrm{.}1(1$ x$)2=13$x$2=$ n $=1$If we wish, we can replace n by n $1$ and write the answer as$1(1$ x$)2=$ n $=0.$According to this theorem, the radius of convergence of the differentiated series is the same as the radius of convergence of the original series, namely, R $=$