| 一类广义Fibonacci数列的通项及求和公式 |
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| 引用本文： | 陈淑贞,张文香.一类广义Fibonacci数列的通项及求和公式[J].海南师范大学学报(自然科学版),2012,25(4):360-363,367. |
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| 作者姓名： | 陈淑贞 张文香 |
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| 作者单位： | 海南师范大学数学与统计学院,海南海口,571158 |
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| 基金项目： | 海南省自然科学基金资助项目（110004） |
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| 摘 要： | 著名的Fibonacci数列有许多通项表达式和性质.本文研究了广义Fibonacci数列{}f（n）∶f（n）=kf（n-1）＋k2f（n-2）,f（0）=1,f（1）=k.利用归纳法和特征方程得到了它的四个通项表达式,同时还利用广义Fibonacci数列{（fn）}的递推性质,获得了它的两个性质和四个求和公式,推广了Fibonacci数列的相关结论.
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| 关 键 词： | 广义Fibonacci数列 性质 通项公式 |
General Term and Summation Formula of a Kind of Generalized Fibonacci Sequence |
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| CHEN Shuzhen,ZHANG Wenxiang.General Term and Summation Formula of a Kind of Generalized Fibonacci Sequence[J].Journal of Hainan Normal University:Natural Science,2012,25(4):360-363,367. |
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| Authors: | CHEN Shuzhen ZHANG Wenxiang |
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| Institution: | ( College of Mathematics and Statistics ,Hainan Normal University,Haikou 571158, China) |
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| Abstract: | There are many general expressions and properties for the famous Fibonacci sequence. A kind of generalized Fibonacci sequence {f（n）}∶f（n）=kf（n-1）＋k2f（n-2）,f（0）=1,f（1）=k was studied in this paper. Four general expressions of the generalized Fibonacci sequence f（n） were presented by using the mathematical induction method and seeking the root of characteristic equation. Meanwhile two properties and four summation formula were also obtained by using recursive properties of the generalized Fibonacci sequence {f（n）} and then the associative conclusions of the Fibo- nacci sequence were extened. |
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| Keywords: | generalized Fibonacci sequence property general expressions |
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