1998年高考试题文、理科第 ( 2 5 )题分别推出不等式( 1+11) ( 1+13 )… ( 1+12 n-1) 2 n+1,( 1+11) ( 1+14 )… ( 1+13 n-2 ) 3 3 n+1,本文将这两个结果统一推广成 :定理　设 {an}是等差数列 ,首项 a1 0 ,公差d1,则对一切自然数 n有( 1+1a1)d an+ 1 a2≤ ( 1+1a1) ( 1+1a2 In 1998, the examination questions and science questions (25) were respectively launched inequality (1+11) (1+13)... (1+12 n-1) 2 n+1, (1+11) (1+14) ... (1+13 n-2) 3 3 n+1, this article will generalize these two results into: Theorem Set {an} is an arithmetic sequence, the first term a1 0, tolerance d1, then for all natural numbers n 1+1a1)d an+ 1 a2≤ (1+1a1) ( 1+1a2