The statement a. is true. However, b. is false (even supposing well defined i.e. for all ) . Choose for example , for all and , for all .
The question is:
Let ( ) and ( ) be monotone sequences. Prove or give a counterexample.
a. The sequence ( ) given by ( )= k* 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 ( ) given by ( )= /[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?