Bounding summations

Give asymptotically tight bounds on the following summations. Assume that $r \ge 0$ and $s \ge 0$ are constants.

1. $\sum_{k = 1}^n k^r$.
2. $\sum_{k = 1}^n \lg^s k$.
3. $\sum_{k = 1}^n k^r \lg^s k$.

Arghh! Laters!