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Erschienen in:
2015 | OriginalPaper | Buchkapitel
1. Numerical series
verfasst von : Claudio Canuto, Anita Tabacco
Erschienen in: Mathematical Analysis II
Verlag: Springer International Publishing
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Abstract
This is the first of three chapters dedicated to series. A series formalises the idea of adding infinitely many terms of a sequence which can involve numbers (numerical series) or functions (series of functions). Using series we can represent an irrational number by the sum of an infinite sequence of increasingly smaller rational numbers, for instance, or a continuous map by a sum of infinitely many piecewise-constant functions defined over intervals of decreasing size. Since the definition itself of series relies on the notion of limit of a sequence, the study of a series' behaviour requires all the instruments used for such limits.