1. The problem statement, all variables and given/known data Let an be monotone sequences. Prove or give a counterexample: The sequence cn given by cn=k*an is monotone for any Real number k. The sequence (cn) given by cn=(an/bn) is monotone. 2. Relevant equations 3. The attempt at a solution On the first one, I don't think the change of sign on k can change the "monotoneness" of the sequence other than by changing decreasing to increasing and vice versa. I have played around using different sequences to see if this is true and it is looking like it is, but I just feel that it could be false. Any ideas?