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Prove that "limit as n approaches infinity |x|^n/n! = 0 for all x"

We are finishing up Maclaurin series but I'm still having a hard time working problems out. I have a quiz on these types of problems in a couple days so anything will be helpful!

1 answer

x^n = x*x*x*x... n times
n! = 1*2*3*... n times
No matter how big x gets, there will be infinitely many factors in the denominator greater than x.

Or, you may note that
∑x^n/n! = e^x
so the terms must converge to zero
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