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本文研究由递增正项等差数列若干项构成的一类不等式 ,为了叙述简便 ,以下约定数列 {an}是公差为d (d 0 )的正项等差数列 ,m ,n为正整数 ,且m1.定理 1 1a1ma2+ 1a2ma3+… + 1anm an + 1md(1ma1- 1m an + 1) .证 由d 0知aiai+ 1(i∈N+ ) .∵ 1ai(1ai+ 1) m -1=1ai· 1ai
In this paper, we study a type of inequality consisting of several items of an increasing positive item series. For the sake of simplicity, the following array {an} is a positive series with a tolerance of d (d 0 ), where m and n are positive integers. M1. Theorem 1 1a1ma2+ 1a2ma3+... + 1anm an + 1md(1ma1 - 1m an + 1) . Proof that d0 knows aaiai+ 1(i∈N+) .∵ 1ai(1ai+ 1) m -1=1ai· 1ai