Question

a bounded sequence in R Which is not convergent ​

Answer 1

Answer:

Step-by-step explanation:

It is bounded because it stays inside the interval [0,1], but it has no limit.

Intuitively, you shouldn't expect that bounded ⟹ convergent, because even if the terms of a sequence stay in some general area, doesn't mean that all of its terms must always be getting closer and closer to each other (which is what the notion of Cauchy sequence captures; a sequence in R or C is convergent ⟺ it is Cauchy).