The order of sum of powers? For example, the sum of n is n(n+1)/2, the dominating term is n square(let say this is order 2). For the sum of n^2, the order is 3. Then for the sum of n^k, is the order k+1? 
I been searching Faulhaber's formula and Bernoulli numbers, I'm not sure what is the order of it. It's much more complicated than i think.
Any ideas? Thanks in advance

By the definition of Riemann integral, $\frac1n \sum_{k=1}^n (\frac{k}{n})^\alpha \rightarrow \int_0^1 t^\alpha dt=\frac1{\alpha+1}$.
Then $\sum_{k=1}^n k^\alpha \sim \frac{n^{\alpha+1}}{\alpha+1}$
