Indefinite sum

Summary

An indefinite sum, or antidifference, of a function $f$ is a function $F$ whose forward difference is $f$, that is $F(x + 1) - F(x) = f(x)$. It plays the role for sums that an antiderivative plays for integrals. With an indefinite sum, every finite sum $\sum_{k=a}^{b-1} f(k)$ becomes the difference $F(b) - F(a)$.