So, when Calculus moves beyond just derivatives and integrals, one way to ease into infinite series is to first look at infinite sequences. In the future, I want to do this with spreadsheets, but for now I use graphing calculators. Here’s an exploration that uses TI83’s or 84’s to get at two key ideas: how to tell if a geometric sequence will converge, and how to tell if an alternating sequence will converge. With those two tools, students can do a lot to make sense of the infinite series that make up Calculus C. It’s your choice how rigorous you wish to make this (do you require them to work out the limits analytically or just express it in common English?) and here is the pdf: SeqConv2019

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