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Homework Help: Limit of sequence (2)

  1. Feb 8, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the limit of this sequence

    An =[itex] \frac{n^{n}}{(n+3)^{n+1}}[/itex]

    2. Relevant equations


    3. The attempt at a solution

    infinite_limit.jpg

    The answer is 0 but my answer is 1

    thank you
     
  2. jcsd
  3. Feb 8, 2013 #2
    Your first step is wrong.
    [tex]\ln \frac{a}{b}≠\frac{\ln a}{\ln b}[/tex]

    The correct property is:
    [tex]\ln \frac{a}{b}= ln a-\ln b[/tex]

    Anyways, instead of taking log on both the sides, you can factor out n from denominator.
     
  4. Feb 8, 2013 #3
    Sorry I cannot see how n can factor out from denominator
     
  5. Feb 8, 2013 #4
    like this ??

    http://postimage.org/image/7cqb5oowp/ [Broken]


    Thanks
     
    Last edited by a moderator: May 6, 2017
  6. Feb 8, 2013 #5
    limit_2.jpg
     
  7. Feb 9, 2013 #6
    What I actually meant was this:
    [tex]\lim_{n→∞} \frac{1}{n+3} \left( \frac{1}{1+\frac{3}{n}} \right)^n[/tex]
     
  8. Feb 9, 2013 #7
    Thank you
     
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