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40-00-AlternatingSeries.tex
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40-00-AlternatingSeries.tex
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\documentclass[12pt]{article}
\usepackage{pmmeta}
\pmcanonicalname{AlternatingSeries}
\pmcreated{2013-03-22 12:27:05}
\pmmodified{2013-03-22 12:27:05}
\pmowner{mathcam}{2727}
\pmmodifier{mathcam}{2727}
\pmtitle{alternating series}
\pmrecord{6}{32587}
\pmprivacy{1}
\pmauthor{mathcam}{2727}
\pmtype{Definition}
\pmcomment{trigger rebuild}
\pmclassification{msc}{40-00}
\pmsynonym{alternating series test}{AlternatingSeries}
\pmrelated{LeibnizsTheorem}
\pmrelated{ProofOfLeibnizsTheorem}
\pmrelated{AlternatingSeriesTest}
\endmetadata
% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%%%\usepackage{xypic}
% there are many more packages, add them here as you need them
% define commands here
\begin{document}
An \emph{alternating series} is a series of the form
$$\sum_{i = 0}^{\infty}(-1)^ia_i$$
or
$$\sum_{i = 0}^{\infty}(-1)^{i+1}a_i$$
where $(a_n)$ is a non-negative sequence. Loosely, this is just a series where the \PMlinkescapetext{terms} ``alternate'' between positive and negative.
For convergence issues, see the following entry: \PMlinkname{alternating series test}{AlternatingSeriesTest}.
%%%%%
%%%%%
\end{document}