What is "geometric series"

n. (context analysis English) infinite series whose terms are in a geometric progression.

n. a geometric progression written as a sum

In mathematics, a geometric series is a series with a constant ratio between successive terms. For example, the series

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

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.