examples of general elementary series.pdf

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1、Examples of General Elementary Series Leif Mejlbro Download free books at LeifMejlbroExamplesofGeneralElementarySeriesCalculus3c-2ExamplesofGeneralElementarySeries–Calculus3c-2©2008LeifMejlbro&VentusPublishingApsISBN978-87-7681-376-5Calculus3c-2ContentsContentsIntroduction51.Partialsumsandtelesc

2、opicseries62.Simpleconvergencecriteriaforseries133.Theintegralcriterion414.Smalltheoreticalexamples475.ConditionalconvergenceandLeibniz’scriterion496.Seriesoffunctions;uniformconvergence81Fast-trackyourcareerMastersinManagementStandoutfromthecrowdDesignedforgraduateswithlessthanoneyearoffull-tim

3、epostgraduateworkexperience,LondonBusinessSchool’sMastersinManagementwillexpandyourPleaseclicktheadvertthinkingandprovideyouwiththefoundationsforasuccessfulcareerinbusiness.Theprogrammeisdevelopedinconsultationwithrecruiterstoprovideyouwiththekeyskillsthattopemployersdemand.Through11monthsoffull

4、-timestudy,youwillgainthebusinessknowledgeandcapabilitiestoincreaseyourcareerchoicesandstandoutfromthecrowd.LondonBusinessSchoolApplicationsarenowopenforentryinSeptember2011.Regent’sParkLondonNW14SAUnitedKingdomFormoreinformationvisitwww.london.edu/mim/Tel+44(0)2070007573Emailmim@london.eduemail

5、mim@london.eduorcall+44(0)2070007573www.london.edu/mim/4Calculus3c-2IntroductionIntroductionHerefollowsacollectionofexamplesofgeneral,elementaryseries.ThereaderisalsoreferredtoCalculus3b.ThemainsubjectisPowerseries;butfirstwemustconsiderseriesingeneral.WeshallinCalculus3c-3returntothepowerseries.

6、Finally,evenifIhavetriedtowriteascarefulaspossible,Idoubtthatallerrorshavebeenremoved.Ihopethatthereaderwillforgivemetheunavoidableerrors.LeifMejlbro14thMay20085Calculus3c-2Partialsumsandtelescopicseries1PartialsumsandtelescopicseriesExample1.1Provethattheseries∞11−n+4n+6n=1isconvergentandfind

7、itssum.Weshallinthischapteronlyusethedefinitionoftheconvergenceasthelimitofthepartialsumsoftheseries.InthisparticularcasewehaveN11sN=−n+4n+6n=111111111=−+−+−+···+−576879N+2N+41111+−+−.N+3N+5N+4N+6Thesumisfinite,