在近年的高考数学试题中 ,常以数列递推式中不等式的证明作为能力型试题 .这类问题综合性强、思维容量大、能力要求高 ,是同学们感到很棘手的一类问题本文通过具体的例子说明解这类问题的几种常用方法 .一、数学归纳法例 1　已知数列 an ,对任意n∈N ,均有an 0 ,且a2 n ≤an-a In the recent college entrance examination mathematics test questions, the proof of inequality in the series of recursive formulae is often used as a competency test item. This type of problem has a strong comprehensiveness, a large capacity of thinking, and a high ability requirement. It is a class of students who find it difficult to answer questions. Specific examples illustrate several commonly used methods to solve such problems. First, the mathematical induction of the law of the law known in the list of an, for any n ∈ N, there are an 0, and a2 n ≤ an-a