Hello,

I need a little bit help with the following power series. The exercise is to calculate the radius of convergence.

$\displaystyle \sum\limits_{n=1}^{\infty} (\mathrm{ln}(n))^{n} x^{n} $

I know the criterion of Euler and the stronger criterion of Hadamard.

Euler:

$\displaystyle r= \frac{\mid a_{n} \mid}{ \mid a_{n+1} \mid }$

Hadamard:

$\displaystyle r= \frac{1}{\mathrm{limsup} ~ \sqrt[n]{\mid a_{n} \mid} } $

and of course $\displaystyle a_{n}$ is

$\displaystyle a_{n} = (\mathrm{ln(n)})^{n}$

My problem now, is that I don't know how to calculate this expressions with this logarithm

Thanks for help