论文部分内容阅读
1.背景(2015高考江苏卷第23题)已知集合X={1,2,3},Y_n={1,2,3,…,n}(n∈N*),设S_n={(a,b)|a整除b或b整除a,a∈X,b∈Y_n},令f(n)表示集合S_n所含元素的个数.(1)写出f(6)的值;(2)当n≥6时,写出f(n)的表达式,并用数学归纳法证明.该题是数学附加题的最后一道题,考点很明确,考查学生由特殊到一般的归纳推理能力,并要求学生用数学归纳法证明所猜想的结论.从考生完成的情况看,能完成第(1)小题的考生不少,对于第(2)小题,能归纳出f(n)的表达式的考生不太多,会用数
1. Background (2015 Entrance Examination Jiangsu Volume 23) Given the set X = {1,2,3}, Y_n = {1,2,3, ..., n} (n∈N *), let S_n = { Let f (n) denote the number of elements contained in the set S_n. (1) Write the value of f (6); ( 2) When n≥6, write out the expression of f (n), and prove it by mathematical induction.This question is the last question of mathematical additional questions, test points is very clear, examine the students from special to general inductive reasoning ability, And require students to use mathematical induction to prove the conjecture of the conclusion from the candidates to complete the situation, to complete the first (1) a small number of candidates, for the second (2), can be summarized f (n) expression Type of candidates is not too much, will use the number