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Proof of Limits: a^(1/n)

  1. Oct 4, 2011 #1
    1. The problem statement, all variables and given/known data
    Let a>1. Prove the limit as n goes to [itex]\infty[/itex] of a1/n = 1.

    3. The attempt at a solution
    Given [itex]\epsilon[/itex] > 0, [itex]\forall[/itex]n>N, |a1/n-L|<[itex]\epsilon[/itex] and N=(a-1)/[itex]\epsilon[/itex].
    |a1/n-L| = a1/n-1

    ...and that's where I get confused. I know that I have to multiply (a1/n-1) by something but I'm not sure what exactly (a hint my professor gave).
  2. jcsd
  3. Oct 4, 2011 #2


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    Homework Helper

    Here's a hint that may or may not help. You want |a^(1/n) - 1| < e. So for example, perhaps you want |a^(1/n) - 1| = e/2.
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