# Elementary symmetric sum

## Definition

The $k$-th symmetric sum of a set of $n$ numbers is the sum of all products of $k$ of those numbers ($1 \leq k \leq n). For example, if$n = 4$, and our set of numbers is$\{a, b, c, d\}$, then: 1st Symmetric Sum =$a+b+c+d$2nd Symmetric Sum =$ab+ac+ad+bc+bd+cd$3rd Symmetric Sum =$abc+abd+acd+bcd$4th Symmetric Sum =$abcd\$

## Uses

Symmetric sums show up in Vieta's formulas