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Sequences

A sequence is an infinite list of numbers, like

 (1)

The numbers in the sequence are called its terms. The general form of a sequence is

where is the -th term of the sequence. In the example (1) above, , , , and so on.

The notations or are abbreviations for

Occasionally the indexing of the terms will start with something other than 1. For example, would mean

(In this case would be the -st term.)

For some sequences, it is possible to give an explicit formula for : this means that is expressed as a function of . For instance, the sequence (1) above can be described by the explicit formula .

Zvezdelina Stankova-Frenkel 2000-09-20