Convergent series doubt

  • Thread starter Ryuzaki
  • Start date
  • #1
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Homework Statement



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

Homework Equations



N/A

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.
 

Answers and Replies

  • #2
938
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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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