摘要
讨论了一个常系数数列,已知递推式求通项公式.先假设该数列为最简单的等差或等比数列,产生矛盾后尝试连续两项满足线性关系的数列,仍然失败,再引入新的数列来代替线性函数中的常数项,再从简单做起,验证引入的新数列为等比数列,逐步推理后得到原数列的通项公式.最后指出了常系数数列的通项公式与常系数微分方程解的关系.
This paper investigates the constant coefficient sequences whose general term is obtained from recursion formulas. Starting with the simplest arithmetic and geometric sequences, this paper then explores the sequences whose any two consecutive terms are related linearly, and new sequences which are developed to replace the constant term. From the simplest way again, the new sequence is proved to be the geometric sequence, and its general term is constructed step by step. This paper also shows the relationship between the general term of the sequence and the solutions of ordinary differential equations with constant coefficients.
出处
《高等数学研究》
2015年第3期18-19,58,共3页
Studies in College Mathematics
基金
解放军理工大学校级教育教学课题(GJ1507038)
关键词
简单
数列
通项
归纳
simple
sequence
general term
summarize
