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Finding Radius of Convergence of the Power Series

  1. Dec 3, 2009 #1
    1. The problem statement, all variables and given/known data
    "Find the radius of convergence of the power series for the following functions, expanded about the indicated point.

    1 / (z - 1), about z = i.



    2. Relevant equations

    1 / (1 - z) = 1 + z + z^2 + z^3 + z^4 + ... +

    Ratio Test: limsup sqrt(an)^k)^1/k



    3. The attempt at a solution

    1 / (z - 1) = -1 / (1 - z) = -1(1 + z + z^2 + z^3 + z^4 + ... +)

    Ratio test gives 1?

    Answer but I'm not sure how sqrt(2)
     
  2. jcsd
  3. Dec 3, 2009 #2

    Mark44

    Staff: Mentor

    Your relevant equation is irrelevant. Your series is not about z = 0 - it's about z = i, so your power series will be in powers of z - i, not powers of z. So your power series should be defined for all z near i. The only value of z where you'll run into problems is z = 1, which happens to be sqrt(2) away from i. Hope that helps.
     
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