Unit: Sequences and SeriesModule: Power Series Definition of Power Serieswww.thinkwell.com firstname.lastname@example.org Copyright 2001, Thinkwell Corp. All Rights Reserved. 1622 –rev 06/15/2001• The general form of a power seriescentered at x=cis ∞=−∑0()nnnaxc, where anis a sequence of numbers that only depend on n. • All power series converge for x=c. If a power series converges for any other values of x, then it converges for all x-values on an interval of convergencecentered at x=c. A power seriesis the infinite sum of successive powers of a given variable each accompanied by a coefficient. Power series are the generalization of Taylor and Maclaurin series.
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