TITLE: Example of a divergent sequence
QUESTION [5 upvotes]: I want to produce a divergent sequence for which $|x_n - x_{n-1}| \to 0$. So far, I've only been able to show that $$\frac{x_n}{n} \to 0$$, which doesn't really help.

REPLY [11 votes]: Another example would be $x_n=\ln n$, since 
$\ln n\rightarrow\infty$ but $\ln n-\ln(n-1)=\ln\frac{n}{n-1}\rightarrow\ln 1=0$.