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.

We use that $$\log x=\int_1^x t^{-1}dt$$
Let $\alpha>0$; choose $0<\varepsilon <\alpha$. Then $$\frac{\log x}{x^{\alpha}}=\frac{1}{x^{\alpha}}\int_1^x t^{-1}dt<\frac{1}{x^{\alpha}}\int_1^x t^{\varepsilon-1}dt<\frac{x^{\varepsilon-\alpha}}{\varepsilon}\to 0$$
