Given a non-negative integer n, return the sum 1 + 2 + 3 + ... + n. The loopAddition LoopWalking i from 1 to n, adding each value to a running total. version is the direct reading of what "sum of the first n numbers" means. Gauss's formulaGauss's Formulan × (n + 1) / 2 — pairing the smallest and largest remaining numbers (1 with n, 2 with n-1, ...), each pair summing to n+1, with n/2 such pairs., famously discovered by Carl Friedrich Gauss as a schoolboy, skips the loop entirely: it's one multiplication and one division, no matter how large n is — a genuine O(1) solution to an O(n)-looking problem.