今年全国高考 (理科 )第 2 0题 :已知 i,m,n是正整数 ,且 1 i≤ mn.( )证明 ni Pimmi Pin;( )证明 ( 1 + m) n( 1 + n) m.不等式 ( )的证明 ,标准答案提供的证法需借助 ( )的结论 ,利用二项式定理证明 ,颇有难度 .事实上无须借助 ( )的结论 ,亦可利用算术 -几何平均值 This year’s National College Entrance Examination (Science) No. 20: Know that i, m, n are positive integers, and 1 i ≤ mn.( ) proves that ni Pimmi Pin;( ) proves (1 + m) n( 1 + n) m. The proof of inequality (), the proof provided by the standard answer requires the help of the conclusion of (), using the binomial theorem to prove, quite difficult. In fact, without using the () result, you can also use the arithmetic-geometric mean