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!

Radius of convergence

  1. Jan 30, 2012 #1
    [tex]\sum_{n=2}^{\infty}z^n\log^2(n), \ \text{where} \ z\in\mathbb{C}[/tex]

    [tex]\sum_{n=2}^{\infty}z^n\log^2(n) = \sum_{n=0}^{\infty}z^{n+2}\log^2(n+2)[/tex]

    By the ratio test,


    [tex]\lim_{n\to\infty}\left|z\left(\frac{\log(n+3)}{ \log (n+2)}\right)^2\right| = |z|[/tex]

    if [itex]|z|<1[/itex], then the sum converges, and if [itex]|z|>1[/itex], then the sum diverges.

    Does this mean that [itex]R=1[/itex]?
    Last edited: Jan 30, 2012
  2. jcsd
  3. Jan 30, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Yes, and there was no need to shift the indices.
  4. Jan 30, 2012 #3
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: 1)

  2. Radius of Convergence (Replies: 4)

  3. Radius of Convergence (Replies: 4)

  4. Radius of convergence (Replies: 7)

  5. Radius of convergence (Replies: 6)