Divergence Test
The divergence test is pretty much the least useless one. All it does is that it checks if a Series is not convergent. The idea is that a series
$$ S = \sum_{n=0}^\infty a_n $$
converges if $\lim_{n\to\infty} a_n = 0$. However, since this is not an if and only if statement, all it says that is if $\lim_{n\to\infty} a_n \neq 0$, then the series is divergent.