[1]赵显曾,冯世,程乃毅.调和级数的收敛子级数的和[J].东南大学学报(自然科学版),1985,15(3):95-106.[doi:10.3969/j.issn.1001-0505.1985.03.012]
 Zhao Xianzeng,Feng Shiyi Cheng Naiyi.The Sum of a Convergent Subseries of the Harmonic Series[J].Journal of Southeast University (Natural Science Edition),1985,15(3):95-106.[doi:10.3969/j.issn.1001-0505.1985.03.012]
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调和级数的收敛子级数的和()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
15
期数:
1985年第3期
页码:
95-106
栏目:
本刊信息
出版日期:
1985-09-20

文章信息/Info

Title:
The Sum of a Convergent Subseries of the Harmonic Series
作者:
赵显曾冯世程乃毅
南京工学院数学力学系; 南京化学工业公司电算站; 南京化学工业公司电算站 讲师; 工程师
Author(s):
Zhao Xianzeng Feng Shiyi Cheng Naiyi
Department of Mathematics and Mechanics, Computer Station of Research Institute of Nanjing Chemical Industrial Company
关键词:
调和级数 子级数 近似值 数字 收敛性 自然数 级数和 存在唯一 构造性 定理
分类号:
+
DOI:
10.3969/j.issn.1001-0505.1985.03.012
摘要:
记 S^p、S^*、S^{(e)}为调和级数sum(1/n)from n=1 to ∞中分别剔除含有数字p(p=0,1,……9)、奇数数字、偶数数字的所有项而成的子级数。本文用构造性的方法不仅估计了这些子级数的和,而且给出了求其近似值的有效方法。
Abstract:
Let S^p,S^* and S(e) denote respectively the Subseries,deleted all the terms whose denominators have a p, an odd number and an even number, from the harmonic series sum n=1 from to ∞ 1/n.By an elementary treatment,this paper gives not only a development to estimate the sums of these subseries,but a process to find their satisfactory approximations also.By this method,we obtain the following results: 1.962608412<S^*<1.962608414, 3.1717654733<S^e<3.1717654735, 22.920635<S^9<22.920679, 23.1034474<S^0<23.1034479.
更新日期/Last Update: 2013-05-01