连续自然数平方根求和的估值问题  

Estimation of the sum of the square-roots of consecutive natural numbers

作　　者：王兴波[1] 

机构地区：[1]佛山科学技术学院机电系,广东佛山528000

出　　处：《佛山科学技术学院学报（自然科学版）》2013年第5期9-13,共5页Journal of Foshan University(Natural Science Edition)

基　　金：广东省工业攻关项目(2012B010600018);广东省数控一代机械产品创新应用示范工程专项资金项目(2012B011300068);佛山市科技发展专项资金项目(2011AA100021);佛山市产学研专项资金项目(2010C012;2012HC100131);禅城区科技计划项目(2011A1025;2011A1030);禅城区产学研专项资金项目(2011B1023)

摘　　要：对连续自然数平方根求和的估值问题进行了研究。首先采用多种方法对问题进行了分析与推演,然后综述了国内外相关的研究结果并对所得的多种结果进行了比较与评估。研究表明,所提问题具有强烈的方法依赖性,且现有结果仍有优化和完善的需要。鉴于此,推荐了2个较好的结果并给出了一个问题在数论方面的应用实例。The paper makes an investigation on the problem of estimation of the sum of the square- roots of consecutive natural numbers. It first utilizes several different approaches to analyze and deduce the problem, then presents a review of current researches on the problem. Through a comparison and an evaluation of the present results, the paper shows that the problem is strongly approach-dependent and further researches and improvements are still necessary. Consequently, the paper proposes two ＇better＇ estimations and an instance of the problem being applied in number theory.

关 键 词：连续自然数 平方根 求和 估值 

分 类 号：O156[理学—数学]