SEQUENCES

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Def. Let S be any non – empty set. A function whose domain is the set of natural numbers and whose range is a subset of S, is called a sequence in the set S.

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Real Sequence: A sequence whose domain is a set of natural numbers and whose range is subset of R is called a Real sequence or a sequence of a real numbers.

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If s is a sequence, then the image s(n) of n ∈ N is usually denoted by      . It is customary to denote the s by the symbol <     > or by {    } . The image s-n of n is called the nth term of the sequence.

And if f is a sequence, then <    >

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Range of a sequence: The set of all distinct terms of a sequence is called its Range.

1. < 1/n> is the sequence <1, 1/2, 1/3, 1/4,………..1/n>. With infinite Range.

2. <n> is the sequence <1, 2, 3, 4, ………..,n >.With Infinite Range.

3. <(-1)^n is the sequence < -1, 1, -1, 1,…………,). Its range is {-1, 1}.With Finite Range.

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