{"title":"Summing Squares and Cubes Using Triangular Numbers","authors":"Roger Nelsen","doi":"10.1080/07468342.2023.2264720","DOIUrl":null,"url":null,"abstract":"SummaryFormulas for the sums of the squares and for the cubes of the first n positive integers are usually proved by mathematical induction. We present alternative proofs using triangular numbers. AcknowledgmentThe author wishes to thank an anonymous reviewer and the Editor for helpful suggestions on an earlier draft of this Capsule.","PeriodicalId":38710,"journal":{"name":"College Mathematics Journal","volume":"66 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"College Mathematics Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/07468342.2023.2264720","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Social Sciences","Score":null,"Total":0}
引用次数: 0
Abstract
SummaryFormulas for the sums of the squares and for the cubes of the first n positive integers are usually proved by mathematical induction. We present alternative proofs using triangular numbers. AcknowledgmentThe author wishes to thank an anonymous reviewer and the Editor for helpful suggestions on an earlier draft of this Capsule.
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