Proof limit of the sequence $\lim_{n\to\infty} [\frac{1}{n+1}+\frac{1}{n+2}+...+ \frac{1}{2n}]=\log 2$
The limit of truncated sums of harmonic series, $\lim\limits_{k\to\infty}\sum_{n=k+1}^{2k}{\frac{1}{n}}$