Let $$\sum_{n=m}^{\infty}a_n$$ be a series of non-zero numbers.
• If [...], then the series $$\sum_{n=m}^{\infty}a_n$$ is absolutely convergent (hence conditionally convergent).
• If [...], then the series $$\sum_{n=m}^{\infty}a_n$$ is not conditionally convergent (hence not absolutely convergent).