Sum up these logs

Calculus Level 4

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

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