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求递推数列的通项公式是中学数学教学的一个重要内容,也是近年来高考的热点之一.如何求递推数列的通项公式,不少同志作了一定的探索,得出一些重要的结论.张蓉同学的《几类递推数列通项公式探讨》(发表在《中学教研》(数学)1989年第二期上)一文,(下称张文)利用特征方程作媒介,将递推数列化归为等比数列求其通项.其方法简捷、巧妙,深受广大同学的喜爱.考虑到数学知识的完整性和系统性,笔者现对张文中关于分式递推数列(一次)的通项推导作如下补充.
The general formula of recursive series is an important part of mathematics teaching in middle school, and it is also one of the hot spots in the college entrance examination in recent years. How to find the general formula of recursive series, many comrades have made some explorations and come up with some important ones. Conclusion. Zhang Rong’s “A Discussion of Several Kinds of Recursive Sequence General Formulas” (published in “Secondary Teaching and Research” (mathematics), 1989, second issue). (Hereinafter referred to as Zhang Wen) uses the characteristic equation as an intermediary and will deliver Pushing the number sequence into equal numbers to find its general term. Its method is simple and ingenious, and it is deeply loved by the students. Taking into account the integrity and systematism of mathematics knowledge, the author is now talking about Zhang Wenzhong’s recurrence series (once The general derivation of ) is as follows.