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与数列有关的大小比较问题,是一类综合性较强的题型,已成为数学高考复习的一个重要专题。本文拟对这类问题的解法作一些探讨,供参考。 一、利用差值比较法 这是解答大小比较问题的一种基本方法,其关键是作差后符号的判断。 例1 (’93全国高考题)已知a_1,a_2,…,a_8为各项都大于零的等比数列,公比q≠1,则( )。 (A)a_1+a_8>a_4+a_5 (B)a_1+a_80,且q≠(?), ∴1-q~3与1-q~4同号,即(1-q~3)(1-q~4)>0。
The issue of size comparisons relating to series is a type of comprehensive question that has become an important topic in the review of mathematics. This article intends to discuss some of the solutions to this type of problem for reference. First, the use of the difference comparison method This is a basic method to solve the size comparison problem, the key is to judge the difference after the symbol. Example 1 (’93 National Entrance Examination Questions) It is known that a_1, a_2, ..., a_8 are equal-number sequences whose all items are greater than zero, and the common ratio q≠1 is (). (A)a_1+a_8>a_4+a_5 (B)a_1+a_80, And q≠(?), ∴1-q~3 are the same as 1-q~4, that is, (1-q~3)(1-q~4)>0.