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Power series and finding radius of convergence

  1. Nov 30, 2006 #1
    1. The problem statement, all variables and given/known data
    "Find the radius of convergence and interval of convergence of the series"
    [tex]\sum_{n=0}^\infty \frac{x^n}{n!}[/tex]




    2. Relevant equations

    Ratio Test

    3. The attempt at a solution

    [tex]\lim{\substack{n\rightarrow \infty}} |x/n+1|[/tex]
    (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: Nov 30, 2006
  2. jcsd
  3. Nov 30, 2006 #2
    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
    -------------
    Imagination is more important than knowlegde - A.Einstein
     
  4. Nov 30, 2006 #3
    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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