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example of integral test
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(Example)
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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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"example of integral test" is owned by paolini.
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Cross-references: divergent, integral, series
This is version 2 of example of integral test, born on 2003-05-08, modified 2003-05-08.
Object id is 4253, canonical name is ExampleOfIntegralTest.
Accessed 2911 times total.
Classification:
| AMS MSC: | 40A05 (Sequences, series, summability :: Convergence and divergence of infinite limiting processes :: Convergence and divergence of series and sequences) |
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Pending Errata and Addenda
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