# Thread: Huh? Ratio test contradicts root test?

1. ## 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?

2. 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 $\displaystyle \left( {\sqrt[n]{{\frac{{n^n }}{{n!}}}}} \right) \to e~?$

3. 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.

4. try (rod) stirling's approximation of n!
http://en.wikipedia.org/wiki/Stirling's_approximation

5. Jeez, I had no idea of this stuff. Thanks guys. #### Search Tags

contradicts, huh, ratio, root, test 