1. Not finding help here? Sign up for a free 30min 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!

Am i doing this right?/convergence of sequences

  1. Oct 9, 2011 #1
    1. The problem statement, all variables and given/known data
    [tex]a_n=(\frac{1}{n})^{\frac{1}{\ln{n}}}[/tex]


    2. Relevant equations



    3. The attempt at a solution

    [tex]\lim_{x\rightarrow \infty}(\frac{1}{n})^{\frac{1}{\ln{n}}}[/tex]
    [tex]y=(\frac{1}{n})^{\frac{1}{\ln{n}}}[/tex]
    [tex]\ln{y}=\frac{\ln{\frac{1}{n}}}{\ln{n}}[/tex]
    [tex]\ln{y}=\frac{\ln{1}-\ln{n}}{\ln{n}}[/tex]
    [tex]\ln{y}=\frac{\ln{1}}{\ln{n}}-\frac{\ln{n}}{\ln{n}}[/tex]
    [tex]\ln{y}=0-1[/tex]
    [tex]e^{\ln{y}}=e^{-1}[/tex]
    [tex]\lim_{x\rightarrow \infty}(\frac{1}{n})^{\frac{1}{\ln{n}}}=e^{-1}[/tex]

    the back of my book says the answer is indeed [itex]e^{-1}[/itex] but im not sure if this is the way to go to for the solution or whether im supposed to rewrite it as something similar to [itex]\lim_{x\rightarrow \infty}(1+\frac{x}{n})^{n}[/itex]
     
  2. jcsd
  3. Oct 9, 2011 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You steps are fine. That problem gives a constant sequence, just written in a non-obvious way.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Am i doing this right?/convergence of sequences
  1. Am I doing this right? (Replies: 7)

  2. Am I doing it right? (Replies: 3)

  3. Am i doing this right (Replies: 4)

  4. Am I doing this right? (Replies: 1)

Loading...