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Convergent series doubt

  1. Sep 14, 2012 #1
    1. The problem statement, all variables and given/known data

    Show by example that if Ʃan and Ʃbn are two convergent series, then Ʃ (anbn) may be a divergent series.

    2. Relevant equations


    3. The attempt at a solution

    I've been trying long and hard to find an example for this particular case, but I'm unable to find one. I've found examples where Ʃan and Ʃbn are divergent, but Ʃ(anbn) is convergent. Can anyone please give an example? Thanks.
  2. jcsd
  3. Sep 14, 2012 #2
    I think it's true that if Ʃan and Ʃbn are absolutely convergent, then also Ʃanbn converges. So maybe consider series which are convergent, but not absolutely convergent.
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