1. The problem statement, all variables and given/known data assuming an and bn are cauchy, use a triangle inequality argument to show that cn= | an-bn| is cauchy 2. Relevant equations an is cauchy iff for all e>0, there is some natural N, m,n>=N-->|an-am|<e 3. The attempt at a solution I am currently trying to work backwards on this one, since we know for some m,n>=N where N is a natural 2e>|-an+am|+|bn-bm| Thus, through the triangle inequality this is >=|am-an+bn-bm|=|(bn-an)-(bm-am)|>=|bn-an|-|bm-am|. Am I going completely wrong somewhere, because I am getting very stuck here. To anyone who answers, please only hints, not full answers (I am sure this is customary). Again, many thanks.