Euler 1735 + Maclaurin 1742: sum_{n=a}^b f(n) = integral f + (f(a)+f(b))/2 + sum B_{2k}/(2k)! [f^{(2k-1)}]; Bernoulli-number remainder; basis of asymptotic expansions.
Euler 1735 + Maclaurin 1742: sum_{n=a}^b f(n) = integral f + (f(a)+f(b))/2 + sum B_{2k}/(2k)! [f^{(2k-1)}]; Bernoulli-number remainder; basis of asymptotic expansions.