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Limits as n goes to infinity

  1. Apr 4, 2012 #1
    1. The problem statement, all variables and given/known data

    Screen_shot_2012_04_04_at_9_13_04_AM.png

    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. Apr 4, 2012 #2
    Looks good to me.
     
  4. Apr 4, 2012 #3

    Dick

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    Science Advisor
    Homework Helper

    Looks ok to me.
     
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