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?
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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
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.
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![\left( {\sqrt[n]{{\frac{{n^n }}{{n!}}}}} \right) \to e~?](http://latex.codecogs.com/png.latex?\left( {\sqrt[n]{{\frac{{n^n }}{{n!}}}}} \right) \to e~?)
