The question is:

Let ($\displaystyle a_n$) and ($\displaystyle b_n$) be monotone sequences. Prove or give a counterexample.

a. The sequence ($\displaystyle c_n$) given by ($\displaystyle c_n$)= k*$\displaystyle a_n$ is monotone for any real number k.

I don't think the change of sign on a constant will do more than turn a monotone increasing sequence to a monotone decreasing sequence so this statement is probably true.

b. The sequence ($\displaystyle c_n$) given by ($\displaystyle c_n$)= $\displaystyle a_n$/[tex]b_n[tex] is monotone.

I'm also pretty sure that having opposite signs for the sequences being divided isn't going to change much either. So I suspect I need to show the different cases on this proof is that the general idea?