Convergence Test Summary - SUMMARY OF CONVERGENCE TESTS FOR...

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SUMMARY OF CONVERGENCE TESTS FOR SERIES WITH POSITIVETERMSMAT 21C-B, SPRING 2004CHRISTOPHER TUFFLEYHere’s a summary of the convergence tests for seriesn=1pnwith all terms positive, and somesuggested strategies for dealing with such series. See also the table of tests on page 617 of thetext.In section 10.7 we will develope “absolute” versions of most of these tests to deal with serieswith both positive and negative terms.1.Summary of convergence tests1.1.Thenth term test for divergence.This test applies to all series, whether they haveonly positive terms or not, and it isn’t a convergence test (since you can only use it to say thata series diverges) but it’s worth listing here.(a) If limn→∞anis nonzero or does not exist thenn=1andiverges.(b) If limn→∞an= 0we learn nothing aboutn=1anand must do more work.

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