Abel–Dini–Pringsheim theorem
In calculus, the Abel–Dini–Pringsheim theorem is a convergence test which constructs from a divergent series a series that diverges more slowly, and from convergent series one that converges more slowly. Consequently, for every convergence test based on a particular series there is a series about which the test is inconclusive.
Source: Wikipedia — Abel–Dini–Pringsheim theorem (CC BY-SA 4.0)