Real Analysis

In this article, we prove that a convergent sequence is bounded. A sequence is said to be convergent if it has finite limit. Question: Prove that A Convergent Sequence is Bounded. Proof Let us assume that {xn} is a convergent sequence. So it has finite limit, say L. That is, limn→∞ xn = L. So … Read more

A sequence {xn} is called a bounded sequence if k ≤ xn ≤ K for all natural numbers n. For example, {1/n} is a bounded sequence since 0 < 1/n ≤ 1 for all n. Let us now learn about bounded sequence. Bounded Sequence Definition A sequence {xn} is said to be bounded if k … Read more