The sum of consecutive integers 1,2,3...n is given by the formula 1/2n(n+1). How many consecutive integers, starting with 1, must be added to get a sum of 990?

Answer 1

990 = 0.5n(n+1) -> 1980 = n²+n -> 0 = n²+n-1980

By the quadratic equation, n = (-1 +/- sqrt(1-(4*-1980)))/2 = (-1 +/- sqrt(7921))/2 = (-1 +/- 89)/2

Since n cannot be negative in this context, n = (-1 + 89)/2 = 88/2 = 44