论文部分内容阅读
请先看下面的问题: 设有二等差数列{αn}、{bn},其前n项和Sn与Sn’之比为了5n+3/2n+7,求α9/b9的值. 在对此题的分析和研究中,我们发现等差数列的等差中项有一个简单性质,它可以加以推广应用.请看: 设{αn}是一个等差数列,Sn是其前n项和,则有: S3=3α2,S5=5α3,S7=7α4,…… 一般地有: S2n-1=(2n-1)αn,其中n是自然数. 要证明此结论很简单.根据等差数列的前n项和公式及通项公式得:
Please look at the following questions: There are two equal difference columns {αn}, {bn}, and the ratio of the first n terms to Sn and Sn′ is 5n+3/2n+7, and the value of α9/b9 is found. In the analysis and research of this topic, we found that the equal-differenced item has a simple property, which can be generalized and used. Let’s see: Let {αn} be an arithmetic progression, and Sn be the first n sums. Then there are: S3=3α2,S5=5α3,S7=7α4,... Generally there are: S2n-1=(2n-1)αn, where n is a natural number. To prove this conclusion is very simple. According to the front of the arithmetic series The n term and formula and general term formula are: