Hi,

I am trying to prove:

$\displaystyle

\sum_{k=1}^{n-1} k^p < \frac{n^{p+1}}{p+1} < \sum_{k=1}^{n} k^p

$

I have tried a few things, my problem is that I cannot seem to find a general formula for $\displaystyle \sum_{k=1}^{n-1} k^p$

I know that $\displaystyle \sum_{k=1}^{n-1} k^2 = \frac{n^3}{3}-\frac{n^2}{2}+\frac{n}{6}$

But that is only order 2. I don't know if there is a general method for order p.

Thanks

Regards

Craig.