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. Mar 19, 2009 #1
    Having a hard time with this one: E 1/n^x , have tried too use n^-x=e^(-x ln n) which in turn e^(...) = lim n->OO (1-(x ln n)/n)^n and then go on with finding the centre, but I feel I'm far far off. How to get it like E an(x-c)^n and use the more straight foreward path.
     
  2. jcsd
  3. Mar 19, 2009 #2
    Hi incus!

    The series

    [tex]\sum_{n=0}^{\infty}\frac{1}{n^x}[/tex]

    is not a power series, so it does not have a radius convergence. It does however have a region of convergence (the x so that the series converges). Is x supposed to be a real or complex variable?

    In the case where x is a real variable you can use the integral test to find the region of convergence.

    The case where x is complex can be reduced to the real case by considering the real part of x and the absolute value of the terms in the series.
     
  4. Mar 19, 2009 #3

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You can't ask for a radius of convergence unless you say which point you are expanding around. I'm guessing the actual question is 'for what values of x does the series converge'. Is x complex? Hint: your series is a p-series. And your series defines part of the Riemann zeta function.
     
  5. Mar 20, 2009 #4
    Thanks for steering me in the right direction yyat and Dick. Got blinded by the question.
     
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...