Power series and finding radius of convergence

[cowmoo32]

Homework Statement

"Find the radius of convergence and interval of convergence of the series"
$$\sum_{n=0}^\infty \frac{x^n}{n!}$$

Homework Equations

Ratio Test

The Attempt at a Solution

$$\lim{\substack{n\rightarrow \infty}} |x/n+1|$$
(I can't seem to get the |x/n+1| to move up where it should be)

Here's what I don't understand. What do I do if I have an N left over when I get this far?

 

[Garret122]

After using ration test i get

lim x^(n+1)/(n+1)! *(n)/(x^n)! = (x)/(n+1)

ration of convergence is then n-> infinite |x|/n+1 -> 0

so for every chosen x you will get convergence Then R=infinite

Garret
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Imagination is more important than knowlegde - A.Einstein

 

[cowmoo32]

Thanks man. I just got off the phone with my friend and he told me the same thing. I'm not sure what I was thinking...it's been a long day.