| 用特征方程推导斐波那契数列的通项公式 |
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| 引用本文： | 宋庭武. 用特征方程推导斐波那契数列的通项公式[J]. 安庆师范学院学报(自然科学版), 2010, 16(4): 91-92. DOI: 10.3969/j.issn.1007-4260.2010.04.025 |
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| 作者姓名： | 宋庭武 |
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| 作者单位： | 芜湖信息技术职业学院;安徽师范大学数学计算机科学学院, 安徽芜湖241000 |
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| 基金项目： | 2009年安徽高校省级自然科学研究项目，安徽省教育厅优秀青年人才基金项目 |
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| 摘 要： | 斐波那契数列是一个古老的问题,吸引着无数人的兴趣,而其通项公式则是在这个数列诞生之后很长的一段时间后才用数学归纳法解决的。受微分方程中常系数线性微分方程的代数解法启发,本文采取常系数线性递推方程的特征方程解法推导出斐波那契数列的通项公式。
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| 关 键 词： | 斐波那契数列 特征多项式 特征根 |
Inferring the Formula of Genenral Term of Fibonacci Series with Characteristic Equation |
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| SONG Ting-wu. Inferring the Formula of Genenral Term of Fibonacci Series with Characteristic Equation[J]. Journal of Anqing Teachers College(Natural Science Edition), 2010, 16(4): 91-92. DOI: 10.3969/j.issn.1007-4260.2010.04.025 |
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| Authors: | SONG Ting-wu |
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| Affiliation: | SONG Ting-wu(1.Wuhu Vocational College of Information Technology,2.College of Mathematics and Computer Science of Anhui Normal University,Wuhu 241000,China) |
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| Abstract: | Fibonacci series is an old mathematical problem.It has attracted the interest of numerous mathematicians.And its general formula of this series was derived a long time after the birth of the second.Inspired by the algebraic method for solving linear differential equations induction with constant coefficients. |
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| Keywords: | Fibonacci series characteristic equation characteristic root |
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