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Proving series is convergent/divergent

  1. Mar 4, 2013 #1
    1. The problem statement, all variables and given/known data

    The problem is proving that the following series is convergent or divergent:


    Ʃ 1 / [(n)(n+1)(n+2)]^(1/3)
    n=1

    2. Relevant equations

    The limit or direct comparison test

    3. The attempt at a solution

    lim {1 / [(n)(n+1)(n+2)]^(1/3)} / (1/n)
    n->∞

    I then attempted to simplify this and use l'Hopital's Rule, but the cube root made it too complicated, and I couldn't come to an answer.
     
  2. jcsd
  3. Mar 4, 2013 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    l'Hopital is serious overkill. (n)(n+2)(n+2)=n^3(1)(1+1/n)(n+2/n). Try simplifying.
     
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