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Find the interval of convergence of (x^n)/(n! +1)

  1. May 12, 2013 #1
    1. The problem statement, all variables and given/known data
    My main issue here is that if I use the ratio test I end up with lim (x(n!+1))/((n+1)!+1) n-> ∞

    I don't know how to progress here. I believe that the limit will equal 0 and so it's interval of convergence is from -∞<x<∞ with a Radius of convergence of ∞. Is it safe for me to assume that?

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 12, 2013 #2

    ehild

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    It is never safe to assume anything. Prove it.

    ehild
     
  4. May 12, 2013 #3
    Well that's why I was asking. I'm not sure how to deal with the factorials here.
     
  5. May 12, 2013 #4

    ehild

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    Well, do you know what n! is?

    ehild
     
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