\[\sum_{j=1}^{n-1}j^{\alpha}\sim\zeta\left(-\alpha\right)+\frac{n^{\alpha+1}}{%
\alpha+1}\sum_{s=0}^{\infty}\genfrac{(}{)}{0.0pt}{}{\alpha+1}{s}\frac{B_{s}}{n%
^{s}},\]