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Homework Help: Ratio Test inconclusive with factorial

  1. May 2, 2010 #1
    1. The problem statement, all variables and given/known data

    [tex]\sum(n-1)!/(n+2)![/tex]

    2. The attempt at a solution

    I tried the ratio test and came up with the lim[tex]_{}n\rightarrow\infty[/tex] n/(n+3) = 1 which gives no information on convergence or divergence. I'm trying to find absolute or conditional convergence so what else can I do?
     
  2. jcsd
  3. May 2, 2010 #2
    You can first simplify that sum into 1/[(n+2)(n+1)(n)] = 1/[n^3 +3n^2 + 2n].

    Then do comparison test using another sum: 1/n^3,

    Since the latter is greater than the former and it converges, therefore the original series converges. For absolute convergence, just remember to take the absolute value of the original series.
     
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