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数列是高中数学的重点之一,它既有相对的独立性,又具有一定的综合性和灵活性,也是初等与高等数学的衔接点,因而也是历年高考的重点。考查的内容主要有两个方面,一方面是数列的基本概念,另一方面是数列的运算。下面对常见的几种易错点进行归纳总结,同时结合例题进行剖析,以便今后我们在碰到类似的问题时不至于再出错。一忽视数列首项的重要性导致错误例1,已知数列{an}的前n项之和为Sn=2n2+2n+1,则数列{an}的通项公式_______。错解:an=4n。
The sequence is one of the key points of high school mathematics. It not only has the relative independence, but also has a certain degree of comprehensiveness and flexibility. It is also the convergence point of elementary and advanced mathematics, which is also the focus of the college entrance examination over the years. There are two main aspects of the test, one is the basic concept of the sequence, and the other is the operation of the sequence. Here are some common error-prone points summarized, combined with examples of analysis, so that in the future we encounter similar problems will not go wrong. The importance of neglecting the first item leads to an error Example 1. The sum of the first n terms of the known sequence {an} is Sn = 2n2 + 2n + 1, then the general formula for the sequence {an} is _______. Wrong solution: an = 4n.