Geometric series
Sum of an (infinite) geometric progression / From Wikipedia, the free encyclopedia
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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
is geometric, because each successive term can be obtained by multiplying the previous term by . In general, a geometric series is written as , where is the coefficient of each term and 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 Fourier series, and the matrix exponential.
The name geometric series indicates each term is the geometric mean of its two neighboring terms, similar to how the name arithmetic series indicates each term is the arithmetic mean of its two neighboring terms.