Geometric Series

A geometric series is the sum of a Geometric Sequence
where 'a' is called the first term and 'r' is called the ratio.

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This will create the following geometric series where each successive term is obtained by multiplying the previous term by 1/2.

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This series can be written as

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Summing a Geometric Series

The sum of a geometric series is finite as long as the value of r is less than 1.
Despite the series containing an infinite number of terms they get smaller and smaller.
The sum of the first n terms when r is not equal to 1 is:

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The sum of this series

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would be

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Summing a Geometric Series (to infinity)

The sum to infinity is:

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