1. Sep 14, 2012 #1

   Ryuzaki

   

   1. The problem statement, all variables and given/known data
   
   Show by example that if Ʃa_n and Ʃb_n are two convergent series, then Ʃ (a_nb_n) may be a divergent series.
   
   2. Relevant equations
   
   N/A
   
   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 Ʃa_n and Ʃb_n are divergent, but Ʃ(a_nb_n) is convergent. Can anyone please give an example? Thanks.

    

   Ryuzaki, Sep 14, 2012
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3. Sep 14, 2012 #2

   clamtrox

   

   I think it's true that if Ʃa_n and Ʃb_n are absolutely convergent, then also Ʃa_nb_n converges. So maybe consider series which are convergent, but not absolutely convergent.

    

   clamtrox, Sep 14, 2012

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