| Summary: | Summary
A result is discussed which permits the summing of series whose terms have
more complicated sign patterns than simply alternating plus and minus. The
Alternating Series Test, commonly taught in beginning calculus courses, is a corollary. This result, which is not difficult to prove, widens the series summable
by beginning students and paves the way for understanding more advanced
questions such as convergence of Fourier series. An elementary exposition is
given of Dirichlet’s Test for the convergence of a series and an elementary
example suitable for a beginning calculus class and a more advanced example
involving a Fourier series which is appropriate for an advanced calculus class
are provided. Finally, two examples are discussed for which Dirichlet’s Test
does not apply and a general procedure is given for deciding the convergence or
divergence of these and similar examples.
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