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1990年全国高考数学试题(理工农医类)的压轴题(第26题): 设∫(x)=1g(1十2~x+…+(n-1)~x+n~x/na,其中a是实数,n是任意给定的自然数,且n≥2. (i)如果∫(x)当x∈(-∞,1]时有意义,求a的取值范围; (ii)如果a∈(0,1],证明2∫(x)<∫(2x)当x≠0时成立。该题是考生失分率最高的一道题,特别是第(ii)问很多人不能动笔。不少同志惋惜地说,这道题既难住了一般学生也难住了成绩好的学生。有人还风趣地说,这题难得“残
In the 1990 National Mathematical Exam Questionnaire (Science and Physiology, Agriculture and Medicine), the title question (Item 26): Let ∫(x)=1g(1十2~x+...+(n-1)~x+n~x/na, Where a is a real number and n is any given natural number, and n≥2. (i) If ∫(x) is meaningful when x∈(-∞,1), find the range of a; (ii) If A∈(0,1), prove that 2∫(x)<∫(2x) holds when x≠ 0. This question is the question with the highest score for the candidate, and in particular, (ii) asks that many people cannot write. Many comrades said with regret that this problem was difficult for the average student to live with students who had achieved good results. Some people also said humorously that this problem is very rare.