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Help me find the radius of convergence?

  1. Apr 14, 2012 #1
    1. The problem statement, all variables and given/known data
    Ʃn!(x-1)n
    I need to find the radius of convergence for this summation from n=0 to n=∞


    3. The attempt at a solution
    I started off with the ratio test:

    (n!(n+1)(x-1)(x-1)n)/(n!(x-1)n) = (n+1)(x-1)

    (x-1)lim(n+1)...Now at this point it looks to me like the series does not actually converge, but my book is telling me that it does. Am I looking at something the wrong way? Not actually understanding the problem?
     
  2. jcsd
  3. Apr 14, 2012 #2
    It looks like it converges only at x = 1.
     
    Last edited: Apr 14, 2012
  4. Apr 14, 2012 #3
    Usually you do the ratio test on the part of the sum that doesn't have the factor with x, so in this case with just n!. Simplifying that gets you L = limn→∞(n+1) = ∞ and the radius of convergence is r = 1/L = 0.

    The only x value where it converges is x=1.
     
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