Let $$(a_n)_{n=m}^{\infty}$$ be a sequence of real numbers which are non-negative and decreasing, thus $$a_n \ge 0$$ and $$a_n \ge a_{n+1}$$ for every $$n \ge m$$. Then the series $$\sum_{n=m}^{\infty}(-1)^n a_n$$ is convergent if and only if the sequence [...] converges to 0 as $$n \rightarrow \infty$$.