The beginning of that article is slightly wrong: the compiler should compute N(N-1)/2 (and does), because the original code adds up all the numbers from 0 to N excluding N. The usual formulation in math includes the upper bound: the sum of integers from 1 to N, including N, is N(N+1)/2, so you have to replace N by (N-1) if you want a formula for the sum where the last number is N-1.