real analysis - $ lim_{n to infty} frac{sqrt{n}(sqrt{1} + sqrt{2} + ... + sqrt{n})}{n^2} $

How do I find the following limit?
$$ \lim_{n \to \infty} \frac{\sqrt{n}(\sqrt{1} + \sqrt{2} + ... + \sqrt{n})}{n^2} $$
Can limit be find by Riemann sums?

$$\lim_{n\to \infty}\sum_{k=1}^{n}f(C_k)\Delta{x} = \int_{a}^{b}f(x)\,dx$$
I'm not sure what $f(C_k)$ is.

Answer

Hint:
$$ \lim_{n \to \infty} \frac{\sqrt{1} + \sqrt{2} + ... + \sqrt{n}}{\sqrt{n}}\frac1n= \lim_{n \to \infty} \left(\sqrt{\frac1n} + \sqrt{\frac2n} + \sqrt{\frac3n} +\cdots+\sqrt{\frac{n}{ n}} \right) \frac1n $$
$f(C_k)=\sqrt{\dfrac{k}{n}}$ and $\Delta x=\dfrac1n $.