Wednesday, April 25, 2018

calculus - Prove limntoinftyfracnxn!=0.

I've been having trouble using the definition of a limit to prove limits, and at the moment I am trying to prove that
lim



for all x which are elements of natural numbers.
I'm able to start the usual setup, namely let 0<\epsilon and attempt to obtain \left\lvert\dfrac {n^x}{n!}\right\rvert <\epsilon. I don't really feel like this is correct, and I have absolutely no idea how to go about proving this. Any help at all would be very much appreciated!

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