A sum of all or some of the terms of a sequence. Thus, the series 1 + 4 + 9 + 16 + ... is formed from the sequence 1, 4, 9, 16 ,... A series may or may not converge to a particular value as more and more terms are included. A series is said to be absolutely convergent if the sum of the absolute values of the terms converges; in this case the series converges no matter how the terms of the sum are arranged. Series that are conditionally convergent only converge for some arrangements of the terms and, even then, converge to different values for different arrangements.
A series formed from increasing powers of a variable is a power series; such power series are used to represent many functions.
Related category SERIES AND SEQUENCES
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