# Math Help - Cauchy sequences

1. ## Cauchy sequences

Suppose {an }n≥1 , {bn }n≥1 are Cauchy sequences of real numbers. Carfeully prove that {anbn }n≥1 is Cauchy.
No idea where to start or what to do

2. $|a_nb_n- a_mb_m|= |a_nb_n- a_mb_n+ a_mb_n- a_mbm|\le |a_nb_n- a_mb_n|+ |a_mb_n- a_mb_m|$ $= |b_n||a_n- a_m|+ |a_m||b_n- b_m|$.