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Calculus II - Infinite Series

  1. Sep 18, 2011 #1
    1. The problem statement, all variables and given/known data

    Find the Interval of Convergence for the given series. Check the endpoint behavior carefully sigma[n=0,inf] (n (x-2)^n)/( (n+1)4^n )

    2. Relevant equations



    3. The attempt at a solution

    I was following along with the answer key and they used the ratio test...
    The only problem is that
    [x/4 - 1/2] lim n->inf (n+1)^2 / ((n^2 + 2n) ) = x/4 - 1/2
    because the lim n->inf (n+1)^2 / ((n^2 + 2n) )
    I thought the ratio test was inconclusive if when you took the limit you got 1?
    The answer key than proceeded to solve for x assuming
    x/4 - 1/2 < 1
    can this be done even though the limit equals one?
     
  2. jcsd
  3. Sep 18, 2011 #2
    My bad... I get it now sorry guys...
     
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