Question

Given an example of a sequence that does not have a limit ,or explain carefully why there is no such sequence ​

Answer 1

Answer:

A sequence an has at most one limit: an → L and an → L′ ⇒ L = L′. Proof. By hypothesis, given ǫ > 0, an ≈eL for n ≫ 1, and an ≈e L′ for n ≫ 1. Therefore, given ǫ > 0, we can choose some large number k such that L ≈e ak ≈e L′ .