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Radius of Convergence

  1. Apr 19, 2010 #1
    1. The problem statement, all variables and given/known data
    find the interval of convergence of
    [tex]\sum[/tex][(2k+1)!/((2k)((k!)2)]* [xk]

    2. Relevant equations
    Ratio Test

    3. The attempt at a solution
    I already found that it converges on (-1/2, 1/2) by using power series with b=0 and testing the rest of it as ak. However, I am unsure about the end points. I tried using the ratio test with x = (-1/2) and I get the limit to be 1 so the test fails. What test would I be able to use? Any help is greatly appreciated.
    Last edited: Apr 19, 2010
  2. jcsd
  3. Apr 19, 2010 #2
    And i have no clue why the summation is putting all the stuff in there but it is suppose to say just what is in the text at the end.
  4. Apr 19, 2010 #3


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    Science Advisor
    Homework Helper

    A series can't converge if the limit of the terms doesn't go to zero. Try that test at the endpoints.
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