## Abstract

A sequence is simply a set whose elements are labelled by the positive integers (though a more formal definition is given in the next section). We write a sequence in the form *s* = (s_{1},s_{2}, s_{3},…) where the dots indicate that the list of terms continues indefinitely, so that any term, for instance s_{491}, is available for consideration if required. More explicitly we write *s* = (s_{1}, s_{2}, s_{3},…, s_{n},…) to indicate the *n*^{th} term, or simply *s* = (2*n*) _{1} ^{∞} . But s_{n} alone (no parentheses!) is not the name of a sequence, it is the name of a number which is the *n*^{th} term of a sequence. For instance *s* = (2n - 1) _{1} ^{∞} is the sequence of odd integers, *s* = (1,3,5,…) whose *n*^{th} term is s_{n} = 2*n* - 1.

## Keywords

Cauchy Sequence Convergent Subsequence Peak Point Convergent Sequence Finite Limit## Preview

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