Say I have an alternating series $\sum (-1)^n a\_n$. If $\lim\_{n \rightarrow \infty} a\_n=\infty$ or if it does not tend to $0$, then, does $\sum (-1)^n a\_n$ diverge?? I know that if this holds then $\sum a\_n$ diverges, but if I add this $(-1)^n$ would that still be divergent?