Bounding summationsGive asymptotically tight bounds on the following summations. Assume that \(r \ge 0\) and \(s \ge 0\) are constants.

- \(\sum_{k = 1}^n k^r\).
- \(\sum_{k = 1}^n \lg^s k\).
- \(\sum_{k = 1}^n k^r \lg^s k\).

Arghh! Laters!

Bounding summationsGive asymptotically tight bounds on the following summations. Assume that \(r \ge 0\) and \(s \ge 0\) are constants.

- \(\sum_{k = 1}^n k^r\).
- \(\sum_{k = 1}^n \lg^s k\).
- \(\sum_{k = 1}^n k^r \lg^s k\).

Arghh! Laters!