Geometric series

Sum of an (infinite) geometric progression

In mathematics, a geometric series is a series summing the terms of an infinite geometric sequence, in which the ratio of consecutive terms is constant. For example, the series 1 2 + 1 4 + 1 8 + ⋯ {\displaystyle {\tfrac {1}{2}}+{\tfrac {1}{4}}+{\tfrac {1}{8}}+\cdots } is a geometric series with common ratio ⁠ 1 2 {\displaystyle {\tfrac {1}{2}}} ⁠, which converges to the sum of ⁠ 1 {\displaystyle 1} ⁠. Each term in a geometric series is the geometric mean of the term before it and the term after it, in the same way that each term of an arithmetic series is the arithmetic mean of its neighbors.

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