Past exam of the mathematics course of the University of Oxford / 2015 / Prelims / Mathematics II / 1 / b / ii

Choose the sequenceAfter every index there are positive terms arbitrarily large and negative terms arbitrarily small. Thus every term has both a larger later term and a smaller later term. The former excludes a peak of a sequence $(b_n)$, and the latter excludes a peak of a sequence $(-b_n)$.