Chapter 11 - Section 11.8 - Power Series - 11.8 Exercises - Page 751: 8

$R=0$ ; interval of convergence is $(0,0)$

Let $a_{n}=n^{n}x^{n}$, then $\lim\limits_{n \to \infty}|\frac{a_{n+1}}{a_{n}}|=\lim\limits_{n \to \infty}|\dfrac{(n+1)^{n+1}x^{n+1}}{n^{n}x^{n}}|$ $=\lim\limits_{n \to \infty}|(n+1)x(1+\frac{1}{n})^n|$ $=\lim\limits_{n \to \infty}|(n+1)xe|$ $=\infty$ Hence, $R=0$ ; interval of convergence is $(0,0)$