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Series

  • Mariano Giaquinta
  • Giuseppe Modica

Abstract

Processes of infinite summation or infinite series, or, simply, series have appeared since ancient times. Aristotle (384BC-322BC) in his Physics seems to be aware that the geometric series
$$1 + q + {q^2} + {q^3} + \cdots $$
has a finite sum if |q| < 1. Later François Viète (1540–1603) in fact computed (in 1593)
$$1 + q + {q^2} + {q^3} + \cdots = \frac{1}{{1 - q}}.$$

Keywords

Taylor Series Cauchy Sequence Piecewise Constant Function Geometric Series Positive Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Mariano Giaquinta
    • 1
  • Giuseppe Modica
    • 2
  1. 1.Dipartimento di MatematicaScuola Normale SuperiorePisaItaly
  2. 2.Dipartimento di Matematica ApplicataUniversità degli Studi di FirenzeFirenzeItaly

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