How do I prove that $\ln n > 1$ when $n > 2$? I've tried looking at the Taylor series of the function $\ln x$, which is $$\sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n} (x-1)^n,$$ but wasn't able to extract any useful information out. I haven't tried induction but even if it's possible to prove this via induction, I'd rather see a constructive proof, if it's not too much to ask. Thanks for your help.
Edit: Here $n$ is an integer.

Note that for the logarithm to base $b$, $\log_b b = 1$.
The logarithm (to any base) is a strictly monotonous function and so $\log_b a>1$ if $a>b$.
