A straightforward, geometric perspective allows students in a typical calculus course that covers p-series to understand an important gateway to analysis: the mystery of why some p-series converge and other, seemingly very similar p-series, diverge. In the process, we even arrive at some more advanced bounds for convergent p-series, previously published in this Journal in 2005 by Y. Hansheng and B. Lu.
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Gregory Stodolsky (2024) studied this question.
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