1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    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]

    Last edited by a moderator: May 6, 2017
  6. Feb 8, 2013 #5
  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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Limit of sequence (2)
  1. Limit of a sequence 2 (Replies: 3)