Theorem: Sequence is convergent if an only if that is Cauchy's sequence

I have a problem with proof, I can prove in a one way

$$ \epsilon > 0\\|a_n- a| < \epsilon/2\\|a_m- a_n| = |(a_m- a) - (a_n- a)| \leq |a_m- a| + |a_n- a| < \epsilon $$

I dont know in a other way.