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Power Series n^n)*(x^n)

  1. Nov 27, 2011 #1
    Power Series:(n^n)*(x^n)

    1. The problem statement, all variables and given/known data

    The only step I'm having problem with on this problem is when I take the Lim n→∞ of the problem. I want to know how to cancel the n^n on the denominator during one of the steps.

    2. Relevant equations


    Ʃ (n^n)*(x^n)
    n=1

    3. The attempt at a solution

    lim n→∞ [(n+1)^(n+1)]*[x^(n+1)][itex]/[/itex][(n^n)*(x^n)]

    |x| lim n→∞ [(n+1)^(n+1)][itex]/[/itex]n^n

    That's where I got stuck.
     
  2. jcsd
  3. Nov 27, 2011 #2
    Re: Power Series:(n^n)*(x^n)

    (n+1)n+1 / nn = ( (n+1)n / nn ) * (n+1). Can you see the limit now?
     
  4. Nov 27, 2011 #3
    Re: Power Series:(n^n)*(x^n)

    Oh, I definitely see it now! Thanks. (^o^)/
     
  5. Nov 27, 2011 #4

    Dick

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    Re: Power Series:(n^n)*(x^n)

    Can you show (n+1)^(n+1)/n^n>(n+1)??
     
  6. Nov 27, 2011 #5
    Re: Power Series:(n^n)*(x^n)

    Yeah, I can definitely do that part, I just I had a little trouble looking for the one little section I had trouble with.
     
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