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From: Uno on 11 May 2010 04:17
Cogito wrote:
> I have the commonly taught ones I consider trivial... all colleges
> teach these and all calculus texts do as well. Trivial.
> � "limit of the sequence", "nth term test", or "divergence test"
> � geometric
> � p-series
> � telescoping series
> � ratio test
> � absolute convergence tests
> � alternating series test
> � roots test
> � cauchy integral test
> � direct comparison
> � limit comparison
>
> Then I also know these tests that I had to find on my own. In my own
> research I discovered...
> � ratio limits extremum test (in case ratio test L=1)
> � roots limits extremum test (in case roots test L=1)
> � Raabes test (in case ratio test inconclusive)
> � Bertrands test
> � Gauss's test
> � Abel's test
> � Direchlets test
> � Kummer's test
> � Ermakoff's test
> � Cauchy Condensation test
>
> These I know. Im looking for others, if there are any. No need to
> explain them, just give me something to look up. You cant look up a
> something if you dont know what to type into the search bar.
> Unfortunately, all of my "convergence tests" Google searches turn up
> only the trivial cases from the first list, and sometimes if I look
> hard enough I might find the non-trivial ones from the second list
> too... but I cannot find any others (except for Fourier series tests -
> but I dont care for Fourier series at this point)
>

I'm curious what you think the word "trivial" means. If it describes
the first set of tests, then wouldn't it mean "well-known, sound,
useful, and usually sufficient when used judiciously."
--
Uno
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