Converting from radius of convergence to interval of convergence

Question

Using the root test I have determined that $$\sum n^{-n} x^n$$ has a radius of convergence of infinity and $$\sum n^{n} x^n$$ has a radius of convergence of 0. Does this mean that the respective intervals of convergence are $(-\infty,\infty)$ and $\emptyset$? Do i still have to evaluate the endpoints, and if so, how?

Answer 1

You're done for the first one; there are no endpoints to evaluate. The second one has interval of convergence either $\emptyset$ or $[0,0]$; you need to determine whether $x=0$ leads to a convergent series.