Go backward to Limit Quantor Go up to Top Go forward to Example

Series

Definition: Let a be an infinite sequence over R. The series corresponding to a is the sequence where every element s_n is the sum of the first n+1 elements of a:

series: (N -> R) -> (N -> R)

series(a)n := (sum0 <= i <= n ai).

Consequence: If a = [T]_i, then series(a) = [(sum_{0 <= i <= n} T)]_n.

Sequence of (partial) sequence sums.