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: Recall that if $f$ is integrable on $[a,b]$, then:

$$
\int_a^b f(x)~dx = \lim_{n\to \infty} \dfrac{b-a}{n}\sum_{k=1}^n f \left(a + k \left(\dfrac{b-a}{n}\right) \right)
$$

Can you rewrite the given sum in the above form? What might be an appropriate choice for $a$, $b$, and $f(x)$?
