a) Let (an) be a bounded sequence (not necessarily convergent) and let (bn) be a sequence that converges to zero. Prove that the sequence of products (anbn) converges to zero.

b) Explain why you could not use the Algebraic Limit Theorem.

(My first thought was to use the ALT, so I'm confused. Not sure how to formally prove this, although it seems to make sense at the surface)