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For every `c` in **R**, the sequence [`i`*`c`]_{i} is called an
*arithmetic sequence*. Correspondingly,
series([`i`*`c`]_{i})
is called an *arithmetic series*.

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

series([(which can be proved by induction oni*c]_{i})_{n}= (sum_{0 <= i <= n}i*c) =c*n(n+1)/2.

For instance, for `c`=1, we have

[ i]_{i}= [0, 1, 2, 3, 4, 5, ...], series([ i]_{i})= [0, 1, 3, 6, 10, 15, ...].

Author: Wolfgang Schreiner

Last Modification: December 14, 1999