{"title":"一些令人惊讶的级数和","authors":"Russell A. Gordon","doi":"10.1080/0025570X.2023.2168433","DOIUrl":null,"url":null,"abstract":"Summary We establish the convergence of a family of series for which the usual convergence tests fail. In addition, we show how to use elementary methods to find the sums of the series. A wealth of problems for both calculus students and real analysis students can be obtained from this collection of series and connections can be made to both differential equations and hypergeometric functions.","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some Surprising Series Sums\",\"authors\":\"Russell A. Gordon\",\"doi\":\"10.1080/0025570X.2023.2168433\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Summary We establish the convergence of a family of series for which the usual convergence tests fail. In addition, we show how to use elementary methods to find the sums of the series. A wealth of problems for both calculus students and real analysis students can be obtained from this collection of series and connections can be made to both differential equations and hypergeometric functions.\",\"PeriodicalId\":18344,\"journal\":{\"name\":\"Mathematics Magazine\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics Magazine\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/0025570X.2023.2168433\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics Magazine","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/0025570X.2023.2168433","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Summary We establish the convergence of a family of series for which the usual convergence tests fail. In addition, we show how to use elementary methods to find the sums of the series. A wealth of problems for both calculus students and real analysis students can be obtained from this collection of series and connections can be made to both differential equations and hypergeometric functions.
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