A Critical Study on Sequential Limit of a Sequence: Exploring Convergence and Divergence of Sequences

Abstract

Limits can be defined in any metricor topological space, but are usually firstencountered in the real numbers. the limit of the sequence if the following conditionholds: For each real number , there exists a naturalnumber such that, for every natural number , we have . In other words, for every measure of closeness , the sequence's terms areeventually that close to the limit. The sequence is said to converge to or tend to the limit , written or . If a sequence converges to some limit, then it is convergent; otherwise it is divergent.