现行高中教材中 ,有关“在两个正数间插入若干个正数 ,使它们成等差数列或等比数列”的问题有不少 ,2 0 0 1年全国春季高考题 2 0题也源于此 .现将这两个数列的各种平均数大小关系归纳如下 .定理　在两个正数a ,b (a≠b)之间插入n个正数a1,a2 ,a3 ,… ,an,使这n + 2个数成等差 In the current high school textbooks, there are many questions about “inserting several positive numbers between two positive numbers to make them into arithmetic or arithmetic series”. The 2010 Spring National Entrance Examination Question 20 is also a source. Here, we now summarize the relationship between the magnitudes of the averages of these two series as follows. Theorem inserts n positive numbers a1,a2,a3,...,an between two positive numbers a,b (a≠b). Make the n + 2 numbers into equal differences