40A05-ExampleOfIntegralTest.tex

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\pmcanonicalname{ExampleOfIntegralTest}
\pmcreated{2013-03-22 13:37:11}
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\pmowner{paolini}{1187}
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\pmtitle{example of integral test}
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\pmtype{Example}
\pmcomment{trigger rebuild}
\pmclassification{msc}{40A05}

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\begin{document}
Consider the series
\[
   \sum_{k=1}^\infty \frac 1 {k \log k}.
\]
Since the integral
\[
   \int_1^\infty \frac 1 {x \log x}\, dx 
    = \lim_{M\to \infty} \left[\log (\log(x))\right]_1^M
\]
is divergent also the series considered is divergent.
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