Strategy for Series
Now that we’ve got all of our tests out of the way it’s time to think about organizing all of them
into a general set of guidelines to help us determine the convergence of a series.
Note that these are a general set of guidelines and because some series can have more than one
test applied to them we will get a different result depending on the path that we take through this
set of guidelines. In fact, because more than one test may apply, you should always go
completely through the guidelines and identify all possible tests that can be used on a given
series. Once this has been done you can identify the test that you feel will be the easiest for you
to use.
With that said here is the set of guidelines for determining the convergence of a series.
1.
With a quick glance does it look like the series terms don’t converge to zero in the
limit,
i.e.
does
? If so, use the Divergence Test. Note that
you should only do the divergence test if a quick glance suggests that the series terms may
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 Fall '08
 prellis
 Mathematical Series, series A

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