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Limit at infinity

  1. Oct 20, 2009 #1
    1. The problem statement, all variables and given/known data

    How can I prove that:

    [tex]\lim_{n \rightarrow \infty} n^{\frac{1}{n}}=1[/tex]

    Isn't [tex]\infty^{0}[/tex] indeterminate?

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Oct 20, 2009 #2


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    Yes, it is indeterminant. That's not the end of the story. Indeterminant just means you don't know what the limit is yet. Take the log. Can you prove (1/n)*log(n) approaches 0?
  4. Oct 20, 2009 #3
    That becomes [tex]0*\infty[/tex], isn't that indeterminate as well?
  5. Oct 20, 2009 #4
    Can't you use L'Hopital's rule?
  6. Oct 20, 2009 #5
    Right. Thanks guys!
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