January 18th, 2018, 09:11 PM  #1 
Senior Member Joined: Jul 2011 Posts: 405 Thanks: 16  exponential limit
finding $\displaystyle \displaystyle \lim_{n\rightarrow \infty}\frac{a^n}{n!}, a>0$

January 18th, 2018, 11:32 PM  #2  
Senior Member Joined: Oct 2009 Posts: 889 Thanks: 341  Quote:
$$\sum_{n=0}^{+\infty} \frac{a^n}{n!}$$ converges. This is in fact rather easy by the ratio test. What does that then imply about the sequence?  

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exponential, limit 
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