Elementary symmetric sum

The nth symmetric sum is the sum of a group of numbers, taken n at a time. So if the numbers are a, b, c, and 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

Symmetric sums show up in Vieta's formula