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Question on Radius of Convergence for values of x, when f(x) is x^2

  1. Jul 29, 2011 #1
    1. The problem statement, all variables and given/known data
    This is not so much an entire problem I need help with but just a part.

    It is a power series where after you do the ratio test, you end up with |4x^(2)| < 1, so |x^(2)| < 1/4.

    Since the radius of convergence is |x-a| < R, I end up with -1/4 < x^(2) < 1/4, but because you cannot take the square root of a negative number, I get 0 <= x < 1/2

    So how would I describe the Radius of Convergence in this case? Thanks in advance.


    2. Relevant equations

    |x-a| < R (but in this case after the ratio test you end up with 4x^(2) < 1)

    3. The attempt at a solution

    See what I wrote in A


    EDIT: You can delete this post, I was just spacing on some primary algebra :(

    |x^2| < 1/4 -----> |x| < 1/2, -1/2 < x < 1/2 so radius of convergence is 1/2
     
    Last edited: Jul 29, 2011
  2. jcsd
  3. Jul 29, 2011 #2

    Dick

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    Are you really claiming that -1/4<x^2<1/4, means 0<=x<1/2 so x must be greater than or equal to zero?? That's not true. x=(-1/4) works in your original inequality just fine. Now you tell me, where did you go wrong?
     
  4. Jul 29, 2011 #3
    See my edit :p I'm tired. Realized what I was doing wrong
     
  5. Jul 29, 2011 #4

    Dick

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    Sure. A tired problem. Good job solving your own problem.
     
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