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A series is called geometric if each term in the series is obtained from the preceding one by multiplying it by a common ratio. For example, the series

is geometric, since each term is obtained by multiplying the preceding term by 1/2. In general, a geometric series is of the form

.

Geometric series are useful because of the following result:

The geometric series

is convergent if |*r*| < 1, and its sum is

Otherwise, the geometric series is divergent.

So, for our example above, *a*=1, and *r*=1/2, and the sum of
the series is

.

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