Question

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 the sum of 1081

Answer 1

1/2 * n * (n+1) = 1081

distribute

1/2 n^2 +1/2n -1081=0

factor out 1/2

1/2 (n^2 +n -2162) =0

multiply each side by 2

(n^2 +n -2162) =0

factor

(n-46) (n+47) =0

n=46, n=-47

n cannot be negative

n=46

Answer 46