How do you solve for n in S = (n(n+1))/ 2?

1 Answer
Jun 7, 2016

n = (-1 +- sqrt(1+8S))/(2)

Explanation:

S = (n(n+1))/2

S = (n^2+n)/2

2S = n^2 +n

n^2 + n - 2S = 0

using the quadratic formula for : ax^2 + bx + c = 0,

n = (-b +- sqrt( b^2 - 4ac) ) /(2a)

n = (-1 +- sqrt(1 - 4(1)(-2S)))/2

n = (-1 +- sqrt(1+8S))/(2)