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For every `q` in **R**, the sequence
[`q`^{i}]_{i} is called a *geometric
sequence*. Correspondingly,
series([`q`^{i}]_{i})
is called a *geometric series*.

We have, for every
`n` in **N**,

series([(which can be proved by induction onq^{i}]_{i})_{n}= (sum_{0 <= i <= n}q^{i}) =q^{n}-1/q-1.

For instance, for `q`=2, we have

[ 2^{i}]_{i}= [1, 2, 4, 8, 16, ...], series([ 2^{i}]_{i})= [1, 3, 7, 15, 31].

Author: Wolfgang Schreiner

Last Modification: December 14, 1999