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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