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!

Interval of Convergence

  1. Aug 3, 2012 #1

    knv

    User Avatar

    1. Find the radius and the interval of convergence for the series:

    Ʃ n=2 --> inf : [(-1)nxn]/ [4nln(n)]





    2.To find the radius, we use the alternating series test. **an+1/an




    3. From the alternating series test I find that the limit as n --> inf = 4. So our radius is 4. Although I do not know how to get the intervals from the radius. Can anyone help me?

    Would we just plug in ±4 for x and solve for convergence or divergence?
     
    Last edited by a moderator: Aug 3, 2012
  2. jcsd
  3. Aug 3, 2012 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You mean the ratio test.
    Yes. You know you have convergence for ##-4 < x < 4##. So just check to see which, if any, of the end points to include.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Interval of Convergence
Loading...