$\lim_{n \to \infty} \left(\frac{1}{1+n} + \frac{1}{2+n} + \frac{1}{3+n} + \ldots + \frac{1}{2n}\right)$ is equal to:\\ (1) 0\\ (2) $\log_e 2$\\ (3) $\log_e \frac{3}{2}$\\ (4) $\log_e \frac{2}{3}$