I was recently reading Paul's online notes on the Alternating Series Test. I noticed that he says "for this proof to work we really do need [the absolute value of the terms] to be positive and decreasing for all n" . I was wondering why this test doesn't apply when the terms are positive and decreasing 'eventually' as is the case in the comparison and integral tests.

  • $\begingroup$ Sounds like you are wondering for a good reason. Please show your way of doing it in detail. As it is the question is on the brink of being closed. $\endgroup$
    – Kurt G.
    Commented Apr 2, 2022 at 19:27
  • 1
    $\begingroup$ You're correct that "eventually" decreasing (with limit $0$) is enough. $\endgroup$ Commented Apr 3, 2022 at 4:25


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