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Radius of convergence: 1/(1+x^2) about 1, using only real analysis

  1. Nov 28, 2011 #1
    I've seen this thread:
    https://www.physicsforums.com/showthread.php?t=297842

    and that is the exact question I need to to answer.

    What is the radius of convergence of 1/(1+x^2) expanded about x_0=1?

    The problem is, I can only use an argument in real analysis.

    I see the answer is sqrt(2), but I cannot get that answer.

    I've tried a lot of little manipulations to get different geometric series but I can't seem to get it.

    Thanks
     
  2. jcsd
  3. Nov 28, 2011 #2
    What is the taylor series? What tests did you try? It might be easier to find the radius of convergence of 1/(1+x) about 1.
     
  4. Nov 28, 2011 #3
    I don't see an easy formula for the nth derivative so I'm not sure how to proceed in that direction
     
  5. Nov 28, 2011 #4
    I didn't do 1/(1+x^2) but there is nice form of the nth derivative of 1/(1+x)
     
  6. Nov 28, 2011 #5
    Do you mean I can use that to get a taylor series for my function
     
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