define infinite series
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An infinite series is the sum of the values in an infinite sequence of numbers. In the above examples, the sum of the numbers in N is the series n = 0 + 1 + 2 + 3 + ..., which is is undefined. ... An infinite series is the sum, if defined, of the numbers in a specific infinite sequence.
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An infinite sequence is a list or string of discrete objects, usually numbers, that can be paired off one-to-one with the set of positive integer s {1, 2, 3, ...}. Examples of infinite sequences are N = (0, 1, 2, 3, ...) and S = (1, 1/2, 1/4, 1/8, ..., 1/2 n , ...). The fact that a sequence is infinite is indicated by three dots following the last listed member.
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