Wikipedia has a number of equations for approximating a summation. Unfortunately, there are no proofs or references.
For example: $ \sum_{i=1}^n \log(i)^c i^d b^i = \theta(n^d \log(n)^c b^n) $ for non-negative real $b\gt1$, $c$, $d$.
Does anyone know how to prove this, or where I can find a reference that proves it?