Question

Give an example of a bounded sequence in R which is not convergent.

Answer 1

Step-by-step explanation:

• Theorem 2.4: Every convergent sequence is a bounded sequence, that is the set {xn : n ∈ N} is bounded. Remark : The condition given in the previous result is necessary but not sufficient. For example, the sequence ((−1)n) is a bounded sequence but it does not converge.