Sum up these logs

Calculus Level 4

\[\displaystyle \lim_{n\rightarrow \infty} \dfrac{1}{n} \left[ \ln(1) + \ln\left( 1 + \dfrac{1}{n} \right) + \ln\left( 1 + \dfrac{2}{n}\right) + \ldots + \ln(2) \right] = \ ? \]

\[\ln e\] \[\ln\left(\dfrac{4}{e}\right)\] \[3 \ln 2 - \ln 4\] \[\ln 2 - \ln e\] None of these \[\ln 4\] \[\ln 4 + 1\]