Consider a sequence $a_n \ge 0$, $a_n \to +\infty$. Here, I'll say that a series $\sum{b_n}$ diverges if $\lim_{N\to \infty}{\sum_{n = 0}^N{b_m}} = \pm \infty$, and that doesn't converges if this limit doesn't exists. My aim is prove that $\sum_{n \ge 0}{(-1)^n a_n}$ can't neither converge (this seems to be pretty easy, and I guess I have shown it) nor diverge. So, my questions are
(a) Is that statement true?
(b) How can I exclude the divergence of the series (if possible)?