Definition:Summation/Indexed

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 $S$.

The composite is called the indexed summation of $\left({a_1, a_2, \ldots, a_n}\right)$, and is written:


 * $\displaystyle \sum_{j \mathop = 1}^n a_j = \left({a_1 + a_2 + \cdots + a_n}\right)$

Also see

 * Definition:Summation over Finite Set