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Thread: Cauchy sequences

  1. September 20th 2010, 05:21 PM #1
    calculuskid1
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    Cauchy sequences

    Suppose {an }n≥1 , {bn }n≥1 are Cauchy sequences of real numbers. Carfeully prove that {anbn }n≥1 is Cauchy.
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  2. September 21st 2010, 03:34 AM #2
    HallsofIvy
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    |a_nb_n- a_mb_m|= |a_nb_n- a_mb_n+ a_mb_n- a_mbm|\le |a_nb_n- a_mb_n|+ |a_mb_n- a_mb_m| = |b_n||a_n- a_m|+ |a_m||b_n- b_m|.
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