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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([i*c]i)n = (sum0 <= i <= n i*c) = c*n(n+1)/2.(which can be proved by induction on n).
For instance, for c=1, we have
[i]i = [0, 1, 2, 3, 4, 5, ...], series([i]i) = [0, 1, 3, 6, 10, 15, ...].