Description

In discussing the tests for convergence or divergence of an infinite series there are often quite a few hypotheses that must be considered in order to get to the conclusion. Now the reason for all of these hypotheses (or as I used to refer to them as “front loading’) is usually made evident in the proof of the specific test that is being discussed. However, most instructors (me included) do not always provide proofs for each of these tests during lecture (most of my students are extremely grateful for that fact). What this unfortunately often leads to is students questioning WHY they must show a bunch of conditions must be verified before they can reach a converge or diverge conclusion, or worse they assume that some of the hypotheses are redundant (when they are not) and so forget to check them at all. In this talk I would like to show a few examples that may be able to quickly remedy these questions. In lieu of showing the proofs, a few carefully crafted examples might just preemptively avoid problems and questions before they arise.