### Geometric Series

The essence of the situation can be illustrated using a simple geometric series. Let be any real (or complex) number. Then we have

when

In other words, the geometric series
is
guaranteed to be summable when , and in that case, the sum is
given by . On the other hand, if , we can rewrite
as
to obtain
*or*, an anticausal geometric series in (negative) powers of .

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