Question

Can this be used for checking divergence, or is it only convergence?

http://en.wikipedia.org/wiki/Alternating_series_test

Answer 1

When all parts of the alternating series test are fulfilled, you can say that the series conclusively converges. When part(s) of the test is unfulfilled, you can hence say that it diverges (does not converge).

Answer 2

...there are some tests (i.e., the Ratio test) that have certain outcomes which are inconclusive; with that result you aren't able to tell if it's convergent or divergent. However, with the AST, it is a stipulation that you cannot have a series with a_n alternating between positive and negative (after eliminating the (-1)^n term) so if the limit of a_n as n approaches infinity is not zero, and/or a_n is smaller than a_n+1, then you can say that it's a divergent series.