Cauchy's test for convergence

0.01 sec.

Cauchy's test for convergence [kō·shēz ‚test fər kən′vər·jəns]

(mathematics)

A series is absolutely convergent if the limit asnapproaches infinity of itsnth term raised to the 1/npower is less than unity.

A seriesa_nis convergent if there exists a monotonically decreasing function ƒ such that ƒ(n) =a_nforngreater than some fixed numberN, and if the integral of ƒ(x)dxfromNto ∞ converges. Also known as Cauchy integral test; Maclaurin-Cauchy test.

Want to thank TFD for its existence? Tell a friend about us, add a link to this page, add the site to iGoogle, or visit the webmaster's page for free fun content.

?Page tools

Printer friendly
Cite / link

Feedback

Mentioned in	?		Encyclopedia browser	?		Full browser	?
No references found			Cauchy frequency distribution Cauchy horizon Cauchy inequality Cauchy Integral Cauchy integral formula Cauchy integral test Cauchy integral theorem Cauchy mean Cauchy mean-value theorem Cauchy net Cauchy number Cauchy principal value Cauchy Problem Cauchy product Cauchy radical test Cauchy random variable Cauchy ratio test Cauchy relations Cauchy residue theorem Cauchy sequence Cauchy surface Cauchy Theorem Cauchy transcendental equation Cauchy's Inequality Cauchy's mean-value theorem Cauchy's test for convergence Cauchy, Augustin Louis Cauchy, Augustin Louis, Baron Cauchy, Augustin-Louis, Baron Cauchy-Hadamard Theorem Cauchy-Riemann Equations Cauchy-Schwarz inequality caucus Cauda cauda equina caudal caudal artery caudal vertebra Caudata caudate caudate lobe caudate nucleus caudex caudicle Caudill, Boone Caudillo Caudine Forks Caudle, Mrs. Margaret Caudwell, Christopher Cauer filter Cauer form			Cauchy product Cauchy radical test Cauchy Random Variable Cauchy ratio test Cauchy reimann equations Cauchy relations Cauchy residue formula Cauchy residue theorem Cauchy Riemann equations Cauchy root test Cauchy sequence Cauchy sequences Cauchy surface Cauchy theorem Cauchy transcendental equation Cauchy's condensation test Cauchy's Inequality Cauchy's integral formula Cauchy's integral theorem Cauchy's mean theorem Cauchy's mean value theorem Cauchy's mean-value theorem Cauchy's radical test Cauchy's root test Cauchy's test for convergence Cauchy's theorem Cauchy, Augustin Louis Cauchy, Augustin Louis, Baron Cauchy, Augustin Louis, Baron Cauchy, Augustin-Louis, Baron Cauchy-Hadamard theorem Cauchy-Lorentz distribution Cauchy-Quine-Fermat-Dirac Cauchy-Riemann conditions Cauchy-Riemann equation Cauchy-Riemann equations Cauchy-Riemann system Cauchy-Schwarz Inequality Caucisian Caucisian Caucisian CAUCTF caucus caucus caucus caucus caucus Caucus of American InnKeepers Caucus of Emory Black Alumni Caucus on Part-Time Employment Concerns Caucus on Social Theory and Art Education caucused caucused caucused caucuses

Encyclopedia

Free Tools:	For surfers: Free toolbar & extensions \| Word of the Day \| Help For webmasters: Free content \| Linking \| Lookup box \| Double-click lookup

Disclaimer
All content on this website, including dictionary, thesaurus, literature, geography, and other reference data is for informational purposes only. This information should not be considered complete, up to date, and is not intended to be used in place of a visit, consultation, or advice of a legal, medical, or any other professional.