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Radius of convergence

  1. May 25, 2008 #1
    [SOLVED] radius of convergence

    1. The problem statement, all variables and given/known data
    Let D be th region in the xy plane in which the series
    [tex]\sum_{k=1}^{\infty}\frac{(x+2y)^k}{k}[/tex]
    converges. Describe D.


    2. Relevant equations



    3. The attempt at a solution
    By the ratio test, we find the radius of converge of the series in x+ 2y to be 1. So, the series will converge when |x+2y| < 1. This region is a rectangle.

    What is wrong with this?
     
  2. jcsd
  3. May 25, 2008 #2
    Be careful with the ratio test because it only tests for absolute convergence. However you are close. It should be [tex]x+2y < 1[/tex] and [tex]x+2y \geq -1[/tex]. This is not a rectangle. It's a "strip" through the plane.
     
  4. May 25, 2008 #3
    I am an idiot.
     
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