续谈a+1/a与a~n+1/(a~n)的关系

• 作 者: 高晓兵 蔡历亮
• 机 构: 广西壮族自治区钦州市北部湾职业技术学校,浙江省台州市黄岩区高桥中学,
• 出 处: 中小学数学(初中版)
• 发表日期: 2016年11期
• 关键词: 中小学数学 a~n+1 文中 中版 a+1/a 一个问题

《中小学数学》(初中版)2010年第6期刊登的《浅谈a+1/a与a~n+1/a~n的关系》(以下简称文[1])一文中,司志本老师根据文中例1至例4的讨论,得到了如下结论:当a+1/a=±2时,|a+1/a|=|a~n+1/a~n|对任意自然数n都成立.在文[1]的结尾,司老师留下了一些问题供有兴趣的读者进一步探讨,其中一个问题是:当

“Elementary and junior high school mathematics” (junior high school edition) published in 2010 sixth issue “on a + 1 / a and a ~ n +1 / a ~ n” (hereinafter referred to as the text [1] According to the discussion of Cases 1 to 4 in this paper, the teacher has got the following conclusion: for a + 1 / a = ± 2, a + 1 / a | = | a ~ n + 1 / a ~ n | n is established at the end of article [1], the division teacher left some questions for further discussion of interested readers, one of the problems is: when