Comparision asymptotic notation

Question

I can get the result of an asymptotic two expressions by using limit or definitions of Big-Oh. However, I cannot express the following one in terms of $n$.

$$\sum_{i=1}^{n} i^k$$

I want to compare it with $n^{k+1}$.

Answer 1

HINT

Recall that by Faulhaber's formula

$$\sum_{i=1}^n i^{k} = \frac{n^{k+1}}{k+1}+O(n^k)$$