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Polynomial convergence question.

  1. Apr 15, 2007 #1
    1. The problem statement, all variables and given/known data

    To find convergence, why can't I divided by the largest n in the denominator in this problem: SUM n_infinity 1/(n^2 - 4n + 4) ?

    its suggested to use the comparison test.

    (I think SUM stands for E Reimann sum correct?)

    but in this problem, I can easily find convergence by dividing by large n in the denominator: lim n->infinity 3n^2/(7n^2 + 1)

    ?

    any explanation please. thanks.

    2. Relevant equations



    3. The attempt at a solution

    its all above. thanks.
     
  2. jcsd
  3. Apr 15, 2007 #2

    Dick

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    Basically, because one is a limit and one is a sum.
     
  4. Apr 15, 2007 #3
    Okay, so for a limit, its okay to divide by the largest N, but for a sum it is not common?
     
  5. Apr 16, 2007 #4

    HallsofIvy

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    Do you understand why dividing by the largest power of N, in both numerator and denominator helps you find the limit of a sequence? Would that apply to an infinite sum?
     
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