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 = (s1,s2, s3,…) where the dots indicate that the list of terms continues indefinitely, so that any term, for instance s491, is available for consideration if required. More explicitly we write s = (s1, s2, s3,…, sn,…) to indicate the nth term, or simply s = (2n) 1 ∞ . But sn alone (no parentheses!) is not the name of a sequence, it is the name of a number which is the nth term of a sequence. For instance s = (2n - 1) 1 ∞ is the sequence of odd integers, s = (1,3,5,…) whose nth term is sn = 2n - 1.
KeywordsCauchy Sequence Convergent Subsequence Peak Point Convergent Sequence Finite Limit
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