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!

Radius of convergence

  1. Apr 13, 2010 #1
    1. The problem statement, all variables and given/known data

    find the radius of convergence and interval of convergence of the series


    Σ (3x-2)^2 / n 3^n
    n=1


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 13, 2010 #2
    You need to clean up your notation a little bit, but the ROC for this series is easily found using any number of tests. Try the ratio test or the limsup test.
     
  4. Apr 14, 2010 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    [tex]\sum_{n=1}^\infty \frac{(3x-2)^n}{n n!}[/tex]
    is, I think, what you want.

    Ratio test is probably best.
    [tex]a_n= \frac{|3x-2|^n}{n n!}[/tex]
    and
    [tex]a_{n+1}= \frac{|3x-2|^{n+1}}{(n+1) (n+1)!}[/tex]

    so the ratio is
    [tex]\frac{|3x-2|^{n+1}}{(n+1)(n+1)!}\frac{n n!}{|3x-2|^n}= |3x-2|\frac{n}{(n+1)^2}[/tex]
    What is the limit of that as n goes to infinity? If that is less than 1, the series will converge.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Radius of convergence
  1. Radius of Convergence (Replies: 4)

  2. Radius of Convergence (Replies: 4)

  3. Radius of convergence (Replies: 2)

  4. Radius of convergence (Replies: 7)

  5. Radius of convergence (Replies: 6)

Loading...