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!

Summing a series on an interval of convergence

  1. May 4, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the interval of convergence of the series and, within this interval, the sum of the series as a function of x.
    [tex]\sum^{\infty}_{n=0}\frac{(x-1)^{2n}}{4^n}[/tex]
    2. Relevant equations
    N/A
    3. The attempt at a solution
    Finding the interval is easy, using the ratio test it reduces down to
    [tex]|\frac{(x-1)^{2}}{4}|<1[/tex]
    [tex]-1<x<3[/tex]

    However, I have no idea how to do the second part. Any help?
     
    Last edited: May 4, 2010
  2. jcsd
  3. May 4, 2010 #2
    1- You should check the end points to decide the interval.
    2- For the sum, I think you know something called "geomtric series", right?
     
  4. May 4, 2010 #3
    Duh! Thanks.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Summing a series on an interval of convergence
Loading...