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!

Power Series- radius of convergence

  1. Apr 22, 2010 #1
    1. The problem statement, all variables and given/known data
    determine the radius of convergence of the given power series

    [tex]\sum[/tex][tex]^{inf}_{n=1}[/tex][tex]\frac{n!x^n}{n^n}[/tex]

    2. Relevant equations



    3. The attempt at a solution
    I did the ratio test
    then I had to take the 'ln'
    but, my answer is this
    |e|<1 for the series to converge.
    It never happens but according to the answers the radius is 'e'.
     
  2. jcsd
  3. Apr 22, 2010 #2
    oh I think I got it, I didn't have to lhopital lnx in the middle ....
    :\
     
  4. Apr 22, 2010 #3
    Applying the Ratio Test, we have the sequence

    [tex]\frac{(n+1)n^n}{(n+1)^{(n+1)}} = \left(\frac{n}{n+1}\right)^n = \left(\frac{1}{1 + \frac{1}{n}}\right)^n[/tex]

    Taking the limit as n goes to infinity... this might look like a familiar limit. Then recall that the Radius of convergence is the reciprocal of this limit.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Power Series- radius of convergence
Loading...