The intuitive concept of sequences of numbers involves not only a set of numbers but also an order in which these numbers have been placed. This suggests that for each positive integer, there is a number associated in the sequence. Thus, real sequence is a function whose domain is the set N of natural numbers and range a set of real numbers. Our aim in this chapter is to study the convergence of real sequences and then to apply the results to study the convergence behavior of various infinite series.

A function *f : N*→*R* whose domain is the set *N* of all natural numbers and range a set of real numbers is called a *sequence of real number* or simply a *real sequence.*

*If n* ∈ *N*, then *f*(*n*) is generally denoted by ...

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