Thread: 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?

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

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.

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

Jeez, I had no idea of this stuff. Thanks guys.