How to do this limit: $\lim\limits_{n\to \infty}\large\frac{\sum_{k=1}^n k^p}{n^{p+1}}$? $$\large\lim_{n\to \infty}\large\frac{\sum_{k=1}^n k^p}{n^{p+1}}$$
I'm stuck here because the sum is like this: $1^p+2^p+3^p+4^p+\cdots+n^p$.
Any ideas?

HINT: This hint is probably a hammer but still worth it.
Faulhaber's formula states that
$$\sum_{k=1}^n k^p = \dfrac1{p+1} \sum_{j=0}^p (-1)^j \dbinom{p+1}j B_j n^{p+1-j}$$
