How to solve limit using Cesaro-Stolz lemma

Question

I have to solve:

$$\lim_{n\to\infty} \frac{\sum_{k=1}^{n}n^p}{n^{p+1}}$$ where $p \in \mathbb{R}$

So far I did the basics but don't know what to do from here:

$$ \lim_{n\to\infty} \frac{(n+1)^p}{(n+1)^{p+1}-n^{p+1}}$$

Answer 1

Recall by binomial theorem that

$$(n+1)^{p+1}-n^{p+1}\sim (p+1)n^p$$