Find the radius of convergence of a given power series.

given $\displaystyle \sum\frac{(x-2)^n}{n^n}$ find the radius of convergence.

so i first substitute y in for x.

and then i use the ratio test.

giving me;

$\displaystyle |y|*\lim_{n\rightarrow\infty} \frac{n^n}{(n+1)^{(n+1)}}$

i don't see any simplifications.

i tried l'Hospitals rule and ended up taking an infinite amount of derivatives to get;

$\displaystyle |y|*\lim_{n\to\infty}\frac{n^n}{(n+1)!}$

which doesn't seem helpful. (even if i didn't flub something along the way which seems unlikely.)

Re: Find the radius of convergence of a given power series.

You should use the root test.

- Hollywood