My book states that the
$$
\lim\_{n\to\infty}\frac{1+\sqrt{2}+...+\sqrt{n}}{n^{3/2}}=
\lim\_{n\to\infty}\frac{1}{n}\left[\frac{1+\sqrt{2}+...+\sqrt{n}}{n^{1/2}}\right]=\frac{2}{3}.
$$
But I just don't see it. I was thinking that if the $$\lim\_{n\to\infty}\frac{1}{n}=0$$ then the whole thing would equal 0 but I don't see how to get $\frac{2}{3}$. Thanks