For series $\displaystyle \sum\limits_{n = 1}^\infty a_n$, it is said to be properly divergent if its partial sum $\displaystyle \sum\limits_{i = 1}^n a_i$ approaches $\displaystyle +\infty$ (or $\displaystyle -\infty$) as $\displaystyle n\to \infty$. Then, is it true that any properly divergent series is still properly divergent under arbitrary rearrangement? Could you please given a proof if it is true or a counterexample if it does not always hold? Thanks!