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Math Help - Cauchy sequences

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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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    |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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