I need to find the convergence interval of the power series and investigate the convergence at the ends of the convergence interval for $$\sum_{1}^{\infty}{\frac{(x^n)^n}{n^n}}$$ I tried to apply the Cauchy convergence test: $$\lim_{n\rightarrow\infty}{\sqrt[n]{\frac{(x^n)^n}{n^n})}} = \lim_{n\rightarrow\infty}{\frac{x^n}{n}}$$ and I don't know what to do with this next.
The answer for this example is: $-1 \leq x \leq 1$.
I would be very grateful if you could point me to a further solution