An example of a bounded pseudo Cauchy sequence that diverges?

Question

Harmonic series diverges and pseudo Cauchy however it's not bounded. So how can I find such a sequence?

A sequence $(s_n)$ is pseudo-Cauchy if, for all $\xi>0$, there exists an $N$ such that if $n ≥ N$, then $|s_{n+1}−s_n| < ξ$.

Answer 1

Try the sequence $$a_n=\sin\sqrt n$$