What is the value of $\lim\limits_{n\to \infty}\left(\sum\limits_{i=1}^n{ \frac{1}{\sqrt{i \cdot n}} } \right)$?
How to evaluate the sum $\frac{1}{\sqrt{n}}+\frac{1}{\sqrt{2n}}+\cdots+\frac{1}{\sqrt{n^2}}$ when $n$ grows?