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Limit Proof

  1. Nov 12, 2009 #1
    1. The problem statement, all variables and given/known data

    How do I prove that lim 2^(1/n) = 1?

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 12, 2009 #2
    What have you done so far?
     
  4. Nov 12, 2009 #3
    This is actually part of a series problem, so I have determined that the sequence of a_n's is decreasing and that it seems to converge to 1. I know that I need to find N \in the naturals such that |2^(1/n)| < epsilon, but I can't seem to figure out how to solve in terms of epsilon.
     
  5. Nov 12, 2009 #4
    Since [itex]2^{1/n}[/itex] is always greater than 1 (prove this!), you can forget the absolute value. Try taking the natural log of both sides of [itex]2^{1/n}-1<\epsilon[/itex] and solving for [itex]n[/itex].
     
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