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Geometric Series

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 = (sum_{0 <= 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].

Author: Wolfgang Schreiner
Last Modification: December 14, 1999

[`2`ⁱ]_i	=	[1, 2, 4, 8, 16, ...],
series([`2`ⁱ]_i)	=	[1, 3, 7, 15, 31].