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 January 18th, 2018, 09:11 PM #1 Senior Member   Joined: Jul 2011 Posts: 400 Thanks: 15 exponential limit finding $\displaystyle \displaystyle \lim_{n\rightarrow \infty}\frac{a^n}{n!}, a>0$
January 18th, 2018, 11:32 PM   #2
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Quote:
 Originally Posted by panky finding $\displaystyle \displaystyle \lim_{n\rightarrow \infty}\frac{a^n}{n!}, a>0$
A very nice way of doing this is to show first that the series
$$\sum_{n=0}^{+\infty} \frac{a^n}{n!}$$
converges. This is in fact rather easy by the ratio test. What does that then imply about the sequence?

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