Answer
$R=1$
$\sum_{n=1}^{\infty}n^{2}x^{n}$
Work Step by Step
$f(x)=\frac{x^{2}+x}{(1-x)^{3}}=\sum_{n=1}^{\infty}n^{2}x^{n}$
$\lim\limits_{n \to \infty}|\frac{a_{n+1}}{a_{n}}|=\lim\limits_{n \to \infty}|\frac{(n+1)^{2}x^{n+1}}{n^{2}x^{n}}|$
$=|x|\lt 1$
The given series converges with $R=1$
