If $K$ is a field complete with respect to a non-archimedean absolute value, then the $n$th term test (checking whether the $n$th term of a series goes to zero) is sufficient to check convergence of a series in $K$.
I was wondering if we have any results that guarantee, under additional hypothesis, whether a series in $\mathbb{R}$ converges by just making sure that the $n$th term goes to zero. An example would be the alternating series test. Are there others?