# Find the radius of convergence of a given power series.

• November 29th 2012, 09:20 PM
bkbowser
Find the radius of convergence of a given power series.
given $\sum\frac{(x-2)^n}{n^n}$ find the radius of convergence.

so i first substitute y in for x.

and then i use the ratio test.

giving me;

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

i don't see any simplifications.

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

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

which doesn't seem helpful. (even if i didn't flub something along the way which seems unlikely.)
• November 30th 2012, 12:56 AM
hollywood
Re: Find the radius of convergence of a given power series.
You should use the root test.

- Hollywood