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Finite Geometric Series

A finite geometric series is the sum of finitely many consecutive terms of a geometric sequence. For r!=1,

sum_(k=0)^(n-1)ar^k=a(1-r^n)/(1-r).

The identity follows by subtracting r times the sum from the original sum, leaving a-ar^n. For r=1, the sum is na. Unlike an infinite geometric series, the finite sum is defined for every real or complex ratio r.

See also

Geometric Progression, Geometric Sequence, Geometric Series

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References

Graham, R. L.; Knuth, D. E.; and Patashnik, O. Concrete Mathematics, 2nd ed. Reading, MA: Addison-Wesley, 1994.

Cite this as:

Weisstein, Eric W. "Finite Geometric Series." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FiniteGeometricSeries.html

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