Euler-Maclaurin Summation Formula

Theorem
Let $f$ be a real function which is appropriately differentiable and integrable.

Then:

where:
 * $f^{\paren k}$ denotes the $k$th derivative of $f$
 * $B_n$ denotes the $n$th Bernoulli number.

Also known as
The Euler-Maclaurin Summation Formula is also seen referred to as the Euler Summation Formula.

Also see

 * Integral Test