The Comparison Test: Not Just for Nonnegative Series
Michele Longo, Vincenzo Valori · Mathematics Magazine · 2006
Consider the following question. Is it possible to generalize the Comparison Test to generic real series? At first glance, many (certainly the authors) could argue something like If it were true then it certainly would be written in some of the books standing on the shelves in my room. As a matter of fact, all the books on the authors' shelves state the test only for nonnegative series. However, a straightforward generalization of this test is possible and useful to study the convergence of series for which standard tests do not apply as we show in this note.