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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:

$\displaystyle \sum_{j \mathop = 1}^n a_j = \tuple {a_1 + a_2 + \cdots + a_n}$

The $\LaTeX$ code for \(\displaystyle \sum_{j \mathop = 1}^n a_j\) is \displaystyle \sum_{j \mathop = 1}^n a_j .

The $\LaTeX$ code for \(\displaystyle \sum_{1 \mathop \le j \mathop \le n} a_j\) is \displaystyle \sum_{1 \mathop \le j \mathop \le n} a_j .

The $\LaTeX$ code for \(\displaystyle \sum_{\map \Phi j} a_j\) is \displaystyle \sum_{\map \Phi j} a_j .