| 平均数构造的数列性质 |
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| 引用本文： | 张高明.平均数构造的数列性质[J].鞍山科技大学学报,2010(4). |
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| 作者姓名： | 张高明 |
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| 作者单位： | 河套大学; |
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| 摘 要： | 对任意给出的m个正实数,通过连续计算其去掉一个实数后所得数组的算术平均数,得到新的m个无穷数列。讨论了这m个无穷数列的性质,得出这m个无穷数列都收敛于初始数组的算术平均数,并将结论拓展到了通过计算几何平均数、调和平均数、平方平均数所得到的数列的情形。得出结论:对任意一个数组,连续计算去掉一个数据后所得数组的平均数,其数字特征不会发生变化,并且如果从每次计算平均数所得的数组中任取一个数据构成无穷子数列,必定收敛于相应的数字特征。
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| 关 键 词： | 平均数 数列 递推公式 通项公式 |
Sequence properties of average structure |
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| ZHANG Gao-ming.Sequence properties of average structure[J].Journal of Anshan University of Science and Technology,2010(4). |
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| Authors: | ZHANG Gao-ming |
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| Institution: | ZHANG Gao-ming(Hetao University,Bayannaoer 015000,China) |
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| Abstract: | For any given m positive numbers,through the continuous calculation of its arithmetic average of the obtained array after removing a real number,a new m numbers of infinite sequences are obtained.In this paper,the properties of m inifite sequences are discussed,and a conclusion is obtained: m infinite sequences converge to the arithmetic average of initial arrays,and a conclusion is extended to the situation of obtained array by calculating geometry average,harmonic mean and square average.The final conclus... |
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| Keywords: | average sequence recurrence formula general formula |
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