Is every strictly locally monotone sequence strictly monotone?
Sequence , n=1,2,3... is strictly locally monotone if for every integer k>1 either < < OR > > .
Prove every strictly locally monotone sequence is strictly monotone or give counterexample.
Sequence , n=1,2,3... is strictly locally monotone if for every integer k>1 either < < OR > > .
Prove every strictly locally monotone sequence is strictly monotone or give counterexample.
We know for we have (without lose of generality). We also know for we have or . It cannot be the latter for . Thus, . So far we know, . Continue this argument.