How to find the limit of $\frac{\ln(n+1)}{\sqrt{n}}$ as $n\to\infty$? I'm working on finding whether sequences converge or diverge. If it converges, I need to find where it converges to.
From my understanding, to find whether a sequence converges, I simply have to find the limit of the function.
I'm having trouble getting started on this one (as well as one more, but I'll stick to one at a time).
I would appreciate if someone could explain how I should start this one.

I assume you want the limit as $n \to \infty$.  $\ln n$ grows more slowly than any positive power of $n$ as $n \to \infty$, including $\sqrt{n}$.  The $+1$ in $\ln(n+1)$ is basically a distraction.  So the answer is zero.
This is a little like killing a mosquito with a sledgehammer, but the conditions of L'Hopital's Rule are met (check them), you can apply it, and it works out nicely.
