sum(k, k=1 to n) = n$\frac{n+1}{2}$. Derivation: pair first and last terms: 1+n, 2+(n-1), ..., giving n/2 pairs each summing to n+1. Alternatively, proved by induction. This is the most basic summation formula and appears as a factor in almost every other summation formula. Quick computation: sum(1 to 100) = 100*101/2 = 5050.