Answer
The sequence converges to $\ln{1} = 0$.
Work Step by Step
Write $\ln{(n+1)} - \ln{n}$ as $\ln{(\frac{n+1}{n})} = \ln{(1 + \frac{1}{n})}$. By continuity of limits, we can take the limit inside the natural log. Since the limit of $1 + \frac{1}{n}$ is 1, we see that our sequence converges to $\ln{1} = 0$.
