# Power series and finding radius of convergence (1 Viewer)

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#### cowmoo32

1. The problem statement, all variables and given/known data
"Find the radius of convergence and interval of convergence of the series"
$$\sum_{n=0}^\infty \frac{x^n}{n!}$$

2. Relevant equations

Ratio Test

3. The attempt at a solution

$$\lim{\substack{n\rightarrow \infty}} |x/n+1|$$
(I cant seem to get the |x/n+1| to move up where it should be)

Here's what I dont understand. What do I do if I have an N left over when I get this far?

Last edited:

#### 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 waht I was thinking...it's been a long day.

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