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Homework Help: 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.
     
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