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

  • Thread starter JRangel42
  • Start date
  • #1
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Power Series:(n^n)*(x^n)

Homework Statement



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.

Homework Equations




Ʃ (n^n)*(x^n)
n=1

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.
 

Answers and Replies

  • #2
382
4


(n+1)n+1 / nn = ( (n+1)n / nn ) * (n+1). Can you see the limit now?
 
  • #3
17
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Oh, I definitely see it now! Thanks. (^o^)/
 
  • #4
Dick
Science Advisor
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Can you show (n+1)^(n+1)/n^n>(n+1)??
 
  • #5
17
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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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