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Homework Help: Comparison Test problem with infinite series

  1. Apr 23, 2013 #1
    1. The problem statement, all variables and given/known data
    I need to use the Comparison Test or the Limit Comparison Test to determine whether or not this series converges:

    ∑ sin(1/n^2) from 1 to ∞

    2. Relevant equations

    Limit Comparison Test: Let {An} and {Bn} be positive sequences. Assume the following limit exists:
    L = lim[n→∞] An/Bn
    if L>0, then ƩAn converges iff ƩBn converges.
    if L = ∞ and ƩAn converges, then ƩBn converges.
    if L = 0 and ƩBn converges, then ƩAn converges.

    Comparison Test: Assume that there exists M > 0 such that 0 ≤ An ≤ Bn for n ≥ M.
    if Ʃ[n=1 to ∞] Bn converges, then Ʃ[n=1 to ∞]An also converges.
    if Ʃ[n=1 to ∞] An diverges, then Ʃ[n=1 to ∞]Bn also diverges.

    3. The attempt at a solution

    I've tried comparing with sin(1/n), sin(n), sin(1/n^3), sin(1/n^4), and a handful of other functions involving sin.

    Sorry, i'm new to the comparison test and limit comparison test :/
  2. jcsd
  3. Apr 23, 2013 #2


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    Homework Helper

    Try comparing with 1/n^2. You know that converges, yes?
  4. Apr 23, 2013 #3
    Thanks, got it now. I was using the Limit Comparison test wrong >.<
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