1. Prove that if a sequence (bn) is bounded and the sum |(an)| going from n= 1 to infinity converges, then the sum of the product of sequences (an)(bn) converges. 2. Relevant equations 3. Given that the sequence bn is bounded it is convergent, and by the absolute convergence test if the sum of the absolute value of the sequence (an) converges then so does the sum of the sequence of (an), therefore the sum of the product of the sequences an and bn converges.