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Number series an bn

  1. Apr 8, 2009 #1
    given two series,
    An and Bn, where one converges and one doesnt in the same limits

    what can be said about
    (An*Bn)
    and (An+Bn)
    in those limits

    for (An+Bn) i said that since[tex]\sum[/tex](An+Bn)=[tex]\sum[/tex]An+[tex]\sum[/tex]Bn
    so since one is infinite the sum must also be

    but for (An*Bn) i dont think the same logic works.
    what can be said about it?
     
  2. jcsd
  3. Apr 8, 2009 #2

    Gib Z

    User Avatar
    Homework Helper

    Well, nothing. It can either converge, or diverge, it depends on what A_n and B_n are. Try thinking of a pair of functions where one converges and the other diverges, but where their product converges, and another pair where it diverges.
     
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