1. The problem statement, all variables and given/known data If the sum(a_n) and the sum(b_n) are both divergent, is the sum(a_n + b_n) necessarily divergent? 3. The attempt at a solution At first I thought it must be divergent, but then I asked, what if a_n is 1/n and b_n is -1/n... then their sum would be 0. Does this logic make sense? And if so, would it imply that sum(a_n + b_n)=0, and is therefore convergent?