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数列是定义在正整数集或其有限子集上的函数,当自变量从小到大依次取值时对应的一列函数值。它的通项公式就是这一函数的解析式。数列以通项为纲,数列问题,常常归结为对数列通项的研究。求数列通项是数列中最基本也是最重要的问题之一,除了直接运用等差等比数列的通项公式外,还经常使用转化思想将未知数列化为已知数列、将复杂数列化为简单数列。有些问题设计新颖、解法多样、技巧性强,有必要介绍一些求通项的常用方法和技巧,帮助读者进行归纳整理,并进一步理解其中蕴含的转化思想。
A sequence is a function defined on a set of positive integers or a finite subset of values that corresponds to a list of arguments when the arguments are in descending order. Its general formula is the analytical function of this function. The sequence as the key link, the sequence of questions, often attributed to the study of the sequence of items. In addition to directly using the general formula of an equal-difference series, it is often used to transform the unknown into a known sequence, the complex sequence into Simple series. Some of the questions are novel in design, diverse in solution and strong in technique. It is necessary to introduce some commonly used methods and techniques for finding common items, help readers to summarize them, and further understand the transformational thoughts contained therein.