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!

Homework Help: 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
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook