Limits as n goes to infinity

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

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    3. The attempt at a solution
    So I know that the limit as [itex]n → ∞[/itex] of [itex](1 - \frac{1}{n})^n = \frac{1}{e}[/itex]. Using this information, is it legitimate to observe:

    The limit as [itex]n → ∞[/itex] of [itex](1 - \frac{1}{n})^{n ln(2)} =[/itex] the limit as [itex]n → ∞[/itex] of [itex]((1 - \frac{1}{n})^n)^{ln(2)} = e^{-1 ln(2)} = e^{ln(\frac{1}{2})} = \frac{1}{2}[/itex]
     
  2. jcsd
  3. Looks good to me.
     
  4. Dick

    Dick 25,893
    Science Advisor
    Homework Helper

    Looks ok to me.
     
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