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January 18th, 2018, 09:11 PM   #1
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exponential limit

finding $\displaystyle \displaystyle \lim_{n\rightarrow \infty}\frac{a^n}{n!}, a>0$
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January 18th, 2018, 11:32 PM   #2
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Originally Posted by panky View Post
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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exponential, limit

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