SOLUTION —
$\begin{array}{l}\lim _{n \rightarrow \infty}\left(\frac{1}{n}+\frac{1}{n+1}+\ldots+\frac{1}{n+2 n}\right) \\\quad=\sum_{r=0}^{2 n} \frac{1}{n+r}=\frac{1}{n} \sum_{r=0}^{2 n} \frac{1}{1+\frac{r}{n}} \\\quad=\int_0^2 \frac{1}{1+x} d x=[\log (1+x)]_0^2=\log 3\end{array}$
So, The correct option will be (B).