Definition:Summation

Definition
Let $\left({S, +}\right)$ be an algebraic structure where the operation $+$ is an operation derived from, or arising from, the addition operation on the natural numbers.

Let $\left({a_1, a_2, \ldots, a_n}\right) \in S^n$ be an ordered $n$-tuple in $S$.

Also known as
It is common for the term sum to be used for summation.

However, despite the fact that summation is longer, and a less-aesthetic neologism for sum, the term summation is preferred on for immediate clarity.

Also see

 * Definition:Product Notation (Algebra)
 * Definition:Composite (Abstract Algebra)
 * Definition:Series