Using a definite integral find the value of $\lim_{n\rightarrow \infty }(\frac{1}{n}+\frac{1}{n+1}+...+\frac{1}{2n})$
The limit of truncated sums of harmonic series, $\lim\limits_{k\to\infty}\sum_{n=k+1}^{2k}{\frac{1}{n}}$