Is Bounded Sequence Convergent?

Since the sequence is bounded above, it converges. It is also true that if a sequence is decreasing (or eventually decreasing) and bounded below, it also converges. an≤a)n+1 for all n≥n0.

Is every bounded sequence a convergent sequence?

Every bounded sequence is NOT necessarily convergent.

Can a bounded sequence diverge?

As far as I know a bounded sequence can either be convergent or finitely oscillating, it cannot be divergent since it cannot diverge to infinity being a bounded sequence.