• Mariano Giaquinta
  • Giuseppe Modica


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)
$$1 + q + {q^2} + {q^3} + \cdots = \frac{1}{{1 - q}}.$$


Taylor Series Cauchy Sequence Piecewise Constant Function Geometric Series Positive Term 
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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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