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数列{an}的第n项an与项数n间的关系可用一个公式an=f(n)来表示,关系式an=f(n)称作该数列的通项公式。“数列的通项”是数列的核心内容之一,也是研究数列、解决数列问题的重要抓手。下面介绍几种常见的数列通项的求法。一、观察归纳法观察归纳法就是根据数列的前几项(或若干项)去发现并归纳出各项(an)与相应项数(n)的一般性关系。例1:根据数列的前4项,写出它的一个通项公式:
The relationship between the nth term an and the number n of the sequence {an} can be expressed as an = f (n). The relation an = f (n) is called the general formula of the sequence. “Number of items ” is one of the core content of the series, but also an important starting point for the study of the series and the solution to the series of questions. Here are a few common sequence of items to solve. First, observe the inductive method of observation Inductive method is based on the first few (or several) to find and sum up (an) and the corresponding number of items (n) of the general relationship. Example 1: Based on the first 4 items of the series, write down one of its general formulas: