Denote \(n\)-nary¹ addition with “the big sigma”

\begin{equation*} \sum_{i = 1}^{n} x_i = x_1 + x_2 + \cdots + x_{n - 1} + x_n, \end{equation*}

or equivalently

\begin{equation*} \sum_{x \in S} x_1 + x_2 + \cdots + x_{n - 1} + x_n \end{equation*}

given the set of terms \(S = \{x_1, x_2, \ldots, x_{n - 1}, x_n\}\).