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mathematical analysis > calculus > series > geometric series

Preferred term

geometric series

Definition(s)

In mathematics, a geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms. For example, the series

${\\displaystyle {\ rac {1}{2}}\\,+\\,{\ rac {1}{4}}\\,+\\,{\ rac {1}{8}}\\,+\\,{\ rac {1}{16}}\\,+\\,\\cdots }$

is geometric, because each successive term can be obtained by multiplying the previous term by ${\\displaystyle 1/2}$ . In general, a geometric series is written as ${\\displaystyle a+ar+ar^{2}+ar^{3}+...}$ , where ${\\displaystyle a}$ is the coefficient of each term and ${\\displaystyle r}$ is the common ratio between adjacent terms. The geometric series had an important role in the early development of calculus, is used throughout mathematics, and can serve as an introduction to frequently used mathematical tools such as the Taylor series, the complex Fourier series, and the matrix exponential.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Geometric_series)

Broader concept(s)

series

In other languages

série géométrique

French

URI

http://data.loterre.fr/ark:/67375/PSR-BT5QN8SM-1

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