Prove the following inequality:

$$\frac{1}{n}+\frac{1}{n+1}+\cdots+\frac{1}{2n-1}\geq \log (2)$$

I have tried experimenting with different values of $n$ and see that the sum seems to converge to $\log(2)$ as $n$ gets larger, but I am having some difficulty proving this inequality. I realize it is probably something to do with the fact that $\frac{d}{dx}\ln(x)=\frac{1}{x}$, but cannot find a proper solution. 

The theme of these problems is that they can generally be solved with some sort of drawing or visual aid, and I am unsure of what I can draw to make this solution more clear.

Any help is appreciated, thanks.