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分类讨论是一种逻辑方法,同时又是一种重要的解题策略,在数学解题中有广泛的应用。所谓分类讨论,是在讨论对象明确的条件下,按照同一的分类标准,不重复、不遗漏、不越级的原则下进行的。它体现了化整为零、积零为整的思想与归类整理的方法。数列中的分类讨论多涉及对公差d、公比q、项数n的讨论,特别是对项数n的讨论成为近几年高考的热点。本文归纳总结出一些常见的用分类讨论思想处理的数列问题。一、求数列通项公式及前n项和公式中,对项数n的讨论例1:(2007年广东高考理5)已知数列{a}n的前n项和Sn=n2-9n,求{a}n的通项公式。分析:本小题要求通项an,题目中已知Sn,则需用an=
Category discussion is a logical method, but also an important problem solving strategy, which has a wide range of applications in solving mathematical problems. The so-called classification discussion is under the conditions of clear discussion of the object, in accordance with the same classification criteria, non-repetition, omission, not the more level of principle. It embodies the idea of sorting out zero and zeroing one by one and the method of sorting and sorting. The discussion of the classification in the series involves more discussion of the tolerance d, the metric q, and the number of terms n, especially the discussion of the number of terms n has become a hot spot in college entrance examination in recent years. This article summarizes some of the common series of issues discussed by the taxonomy of ideas. First, the number of columns through the formula and the first n terms and formulas, the discussion of the number of n Example 1: (2007 Guangdong college entrance examination Li 5) known sequence {a} n the first n and Sn = n2-9n, Seek the general formula for {a} n. Analysis: This topic requires an item, the subject known Sn, you need to use an =