1. The problem statement, all variables and given/known data Suppose that (x_n) is a properly divergent sequence, and suppose that (x_n) is unbounded above. Suppose that there exists a sequence (y_n) such that limit (x_n * y_n) exists. Prove that (y_n) ===> 0. 2. Relevant equations (x_n) ===> 0 <====> (1/x_n) ===> 0 3. The attempt at a solution One can say with certanty that (y_n) must be bounded, as if it weren't, for all K in Naturals, there exists a b_1 in (x_n) > |K| and b_2 > |K|, and there product is unbounded. If (y_n) is bounded, and does not converge to 0, then... what? That's where I'm stuck. How do I finish this? Thanks.