Okay so I have to find the following limit of the function given as :

$$\lim_{n\to\infty} \left(\frac{1}{n}\cdot\frac{2}{n}\cdot\frac{3}{n}\cdots\cdots\frac{n}{n}\right)^\frac{1}{n} $$

Now , on taking $log$ both sides and rearranging , I get something like this

$$ln A =\frac{1}{n} \left[ ln \left(\frac{1}{n}\right)+ln \left(\frac{2}{n}\right)+ln \left(\frac{3}{n}\right)+ \cdot \cdot \cdot \cdot \cdot \cdot \cdot ln \left(\frac{n}{n}\right)\right]$$

OR

$$ln A = \sum_{r=1}^n \frac{1}{n} \cdot ln \left(\frac{r}{n}\right)$$ Now I want to convert it into a Riemann sum , but I have no idea how I can do that , also , what would be the limits of that integral ? Can someone please help me on this ? I'm really new to Riemann sums and using this technique to find limits .