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?

By Writing limit-of-sum as Integral we get 

$$ \displaystyle\lim_{n\to \infty}\large\frac{\sum_{k=1}^n k^p}{n^{p+1}}=\lim_{n\to \infty} \sum_{k=1}^n \frac{k^p}{n\cdot n^p}=\lim_{n\to \infty} \dfrac{1}{n}\sum_{k=1}^n \left(\frac{k}{n}\right)^p=\int_0^1 x^p dx=\frac{1}{p+1}$$

