calculus - How to find the limit of $frac{ln(n+1)}{sqrt{n}}$ as $ntoinfty$?

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.

Answer

Use L'Hospital's rule. Namely, if $\lim_{x\rightarrow a} \frac{f'(x)}{g'(x)}=L$,
then $\lim_{x\rightarrow a} \frac{f(x)}{g(x)}=L$.
In your case just take in terms of x rather than n, so $f(x)=\ln(x+1)$ and $g(x)=\sqrt(x)$, then take the derivatives and find the limit.