# Huh? Ratio test contradicts root test?

• Mar 25th 2009, 09:24 AM
Kaitosan
Huh? Ratio test contradicts root test?
Find the interval of convergence for [(xn)^n]/(2^n * n!)

I've actually tried both methods but they contradict each other! For the root test I got x = 0 and for the ratio test I got x = e/2.

What's going on?
• Mar 25th 2009, 11:15 AM
Plato
Quote:

Originally Posted by Kaitosan
Find the interval of convergence for [(xn)^n]/(2^n * n!)

I've actually tried both methods but they contradict each other! For the root test I got x = 0 and for the ratio test I got x = e/2.

Do you understand that $\left( {\sqrt[n]{{\frac{{n^n }}{{n!}}}}} \right) \to e~?$
• Mar 25th 2009, 11:38 AM
Kaitosan
LOL. I suppose that's my mistake. I thought it was one because the exponent turns into zero. Oh well. Hey, will you please explain how that expression equals zero? Thanks.
• Mar 25th 2009, 11:40 AM
matheagle
try (rod) stirling's approximation of n!
http://en.wikipedia.org/wiki/Stirling's_approximation
• Mar 25th 2009, 01:07 PM
Kaitosan
Jeez, I had no idea of this stuff. Thanks guys. :)