TABLE OF CONTENTS A sequence is a function whose domain is the set N of all natural numbers while the range may be any set S. In other words, a sequence in a set S is a rule which assigns to each natural number a unique element of S.
A real sequence is a function whose domain is the set N of all natural numbers and range a subset of the set R of real numbers.
Symbolically
is a real sequence.
Note. If x : N ? R is a sequence, instead of denoting the image of n ? N by x( n), we shall generally denote it by x n. Thus x 1, x 2, x 3 etc. are the real numbers associated to 1, 2, 3, etc. by this mapping. Also, the sequence x : N ? R is denoted by { x n} or < x n >.
x 1, x 2, ...... are called the first, second ...... terms of the sequence. The mth and nth terms x m and x n for m ? n are treated as distinct even if x m = x n i.e., the terms occurring at different positions are treated as distinct terms even if they have the same value.
The set of all distinct terms of...
