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For every q in R, the sequence [qi]i is called a geometric sequence. Correspondingly, series([qi]i) is called a geometric series.
We have, for every n in N,
series([qi]i)n = (sum0 <= i <= n qi) = qn-1/q-1.(which can be proved by induction on n).
For instance, for q=2, we have
[2i]i = [1, 2, 4, 8, 16, ...], series([2i]i) = [1, 3, 7, 15, 31].