Limit arctan(ln n) I think it's obvious that the limit is $\frac{\pi}{2}$, but I can't figure out how to solve it in a rigorous way, without the use of undetermined expressions involving infinities.
$$\lim_{n\rightarrow \infty}(\arctan(\ln n))$$
Observation: this is the limit of a sequence, therefore $n$ is always an positive integer.

Step 1: Prove that $\displaystyle\lim_{x\rightarrow \infty} \ln x = \infty$
Step 2: Prove that $\displaystyle\lim_{x\rightarrow \infty} \arctan x=\frac{\pi}{2}$
