1. The problem statement, all variables and given/known data Find sequences an and bn such that: an>0 and an→0, Ʃ bn is bounded, but Ʃanbn diverges. 3. The attempt at a solution The idea is that bn should be -1^n or -1^(n+1) and when multiplied by an the odd (larger) terms of the new sequence diverge and overpower the smaller terms. Every sequence an I have tried still ends up converging (for example 1/n → 0 and diverges but (-1^n)/n converges.