In mathematics, a geometric series is a series with 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 1/2.

Geometric series are one of the simplest examples of infinite series with finite sums, although not all of them have this property. Historically, geometric series played an important role in the early development of calculus, and they continue to be central in the study of convergence of series. Geometric series are used throughout mathematics, and they have important applications in physics, engineering, biology, economics, computer science, queueing theory, and finance.