EDIT: sorry about the title of this thread guys.. it was a mistake. if it can be changed please let me know

how can i determine the radius of convergence of the following power series:

$\displaystyle \sum^{\infty}_{n=1}(log n)^2(z - i)^n$

$\displaystyle \sum^{\infty}_{n=1}i^nz^n/n^3$

$\displaystyle \sum^{\infty}_{n=1}n!(z+e)^n$

$\displaystyle \sum^{\infty}_{n=1}n^2z^n/4^n + 3ni$

$\displaystyle \sum^{\infty}_{n=0}z^5n$

Im guessing these have to be done using the ratio test but im not too sure.

any hints please? i will try them out with any clues available thanks.