1. The problem statement, all variables and given/known data If a_n+b_n and a_n-b_n converge then a_n and b_n must converge. This MAY be a counterexample problem. 2. Relevant equations N/A 3. The attempt at a solution I have tried the following possibilities out of a_n and b_n and none of these give a counterexample: Let a_n and b_n= (-1)^n , 1/n , 1/n^2 , (-1)^2n , sqrt(n) I need to come up with something similar to this that holds true that a_n+b_n converge, a_n-b_n converge, but a_n and b_n alone do not converge.