Expressing Express $\lim_{n\to∞} \left(\frac1{n+1} + \frac1{n+2} + ... +\frac1{n+n}\right)$ using Riemann definite integration
The limit of truncated sums of harmonic series, $\lim\limits_{k\to\infty}\sum_{n=k+1}^{2k}{\frac{1}{n}}$