摘要
目的研究Smarandache三角形数及其数列的性质。方法利用初等方法和解析方法对其进行研究。结果研究了三角形数的分部序列的算术平均值及几何平均值的极限问题,获得了这些数列的渐近公式。结论发展了F.Smarandache教授在《Only Problems,Not Solution》一书(Xiquan Publishing House,1993)中涉及的相关研究工作。
Aim To study the properties of triangular numbers and their partial sequences in Only Problems,Not Solution,which was written by Professor F.Smarandache,a Romanian-American number theory expert and it was published by Xiquan Publishing House in 1993.Methods The elementary method and analytic method are adopted to discuss the aforesaid aim.Results By discussing the limit problem of the arithmetic mean and the geometric mean of several partial sequences of triangle numbers,the asymptotic formula of these sequences are obtained.Conclusion The relevant research work has been extended that F.Smarandache professor discussed in Only Problems,Not Solution.
出处
《宝鸡文理学院学报（自然科学版）》
CAS
2011年第1期23-25,共3页
Journal of Baoji University of Arts and Sciences(Natural Science Edition)
基金
国家自然科学基金项目(10671155
10871123)
陕西省自然科学基金项目(SJ08A28)
关键词
三角形数的上部序列
三角形数的下部序列
均值
渐近公式
superior partial sequence of triangular numbers
inferior partial sequence of triangular numbers
mean value
asymptotic formula
