{"title":"用三角数求和平方和立方","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":"{\"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}","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}
Summing Squares and Cubes Using Triangular Numbers
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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