Definition:Summation/Indexed

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

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

The composite is called the summation of $\tuple {a_1, a_2, \ldots, a_n}$, and is written:


 * $\ds \sum_{j \mathop = 1}^n a_j = \paren {a_1 + a_2 + \cdots + a_n}$