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Homework Help: Determining the raidus of convergence

  1. Dec 16, 2013 #1
    1. The problem statement, all variables and given/known data
    Determine the radius of convergence of the given power serie .


    n goes from 0 to infinity

    2. Relevant equations
    limit test ratio

    3. The attempt at a solution
    I am using the limit test ratio and I've got this : [n! * x^(2n+2)]/[(n+1)! * x^2n], then [n!* x^2n * x^2]/[(n+1) * n! * x^2n] , canceling the common things I am left with lim n-> infinity of x^2/n+1, which is 0, but the radius of convergence is infinity, why is infinity?
  2. jcsd
  3. Dec 16, 2013 #2


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    Science Advisor
    Homework Helper

    Because if the ratio test gives you a ratio of r then the corresponding radius of convergence is R=1/r. So as r gets very small the radius of convergence gets very large. If you go all the way to r=0 then R=infinity.
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