{"title":"确定 k 次自然数幂之和的新方法","authors":"V.R. Kalyan Kumar, R. Sivaraman","doi":"10.29121/granthaalayah.v12.i1.2024.5491","DOIUrl":null,"url":null,"abstract":"Since ancient times, mathematicians across the world have worked on different methods to find the sum of powers of natural numbers. In this paper, we are going to present the relationship between sum of kth powers of natural numbers and sum of (k–1) th powers of natural numbers using the differential operator and associated recurrence relation. Interestingly, the Bernoulli numbers which occur frequently in mathematical analysis, play an important role in establishing this relationship.","PeriodicalId":508420,"journal":{"name":"International Journal of Research -GRANTHAALAYAH","volume":"109 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"NOVEL WAY OF DETERMINING SUM OF KTH POWERS OF NATURAL NUMBERS\",\"authors\":\"V.R. Kalyan Kumar, R. Sivaraman\",\"doi\":\"10.29121/granthaalayah.v12.i1.2024.5491\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Since ancient times, mathematicians across the world have worked on different methods to find the sum of powers of natural numbers. In this paper, we are going to present the relationship between sum of kth powers of natural numbers and sum of (k–1) th powers of natural numbers using the differential operator and associated recurrence relation. Interestingly, the Bernoulli numbers which occur frequently in mathematical analysis, play an important role in establishing this relationship.\",\"PeriodicalId\":508420,\"journal\":{\"name\":\"International Journal of Research -GRANTHAALAYAH\",\"volume\":\"109 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-02-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Research -GRANTHAALAYAH\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.29121/granthaalayah.v12.i1.2024.5491\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Research -GRANTHAALAYAH","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.29121/granthaalayah.v12.i1.2024.5491","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
自古以来，世界各地的数学家都在研究不同的方法来求自然数的幂级数之和。本文将利用微分算子和相关的递推关系，介绍自然数 k 次幂之和与自然数 (k-1) 次幂之和之间的关系。有趣的是，在数学分析中经常出现的伯努利数在建立这种关系中发挥了重要作用。
NOVEL WAY OF DETERMINING SUM OF KTH POWERS OF NATURAL NUMBERS
Since ancient times, mathematicians across the world have worked on different methods to find the sum of powers of natural numbers. In this paper, we are going to present the relationship between sum of kth powers of natural numbers and sum of (k–1) th powers of natural numbers using the differential operator and associated recurrence relation. Interestingly, the Bernoulli numbers which occur frequently in mathematical analysis, play an important role in establishing this relationship.
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