Explanation

(b)
$\lim_{n \rightarrow \infty}\left( \frac{1}{n} + \frac{1}{n + 1} + ... + \frac{1}{n + 2n} \right)$
$= \sum_{r = 0}^{2n}{\frac{1}{n + r} = \frac{1}{n}\sum_{r = 0}^{2n}\ \frac{1}{1 + \frac{r}{n}}}$
$= \int_{0}^{2}{\frac{1}{1 + x}dx = \lbrack{\log{(1 + x)\rbrack}}_{0}^{2}}$
$= \log{3 - \log{1 = \log 3}}$