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Radius of convergence

  • Thread starter ehrenfest
  • Start date
  • #1
2,012
1
[SOLVED] radius of convergence

Homework Statement


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.


Homework Equations





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?
 

Answers and Replies

  • #2
148
0
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.
 
  • #3
2,012
1
I am an idiot.
 

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