设1≤k≤n,k,n∈N,则n∑k=1akbk=n-∑1k=1(∑ki=1ai)(bk-bk+1)+bnn∑k=1ak.上述恒等式称为阿贝尔(Abel)部分和公式,其结构优美,背景深刻,在数学分析中有重要应用.本文介绍这一公式在数学竞赛不等式问题中的应用.1联想公式外形,搭乘解题直通车例1设a,b,c,d为非负实数,且a≤1,a+b Suppose 1≤k≤n, k, n∈N, then nΣk = 1akbk = n-Σ1k = 1 (Σki = 1ai) (bk-bk + 1) + bnnΣk = 1ak The above identity is called Abel part and formula, its structure is beautiful, the background is deep, it has important application in mathematical analysis.This article introduces the application of this formula in mathematics race inequality problem.1 The appearance of associative formula, take solving train 1 Let a, b, c, d be nonnegative real numbers, and a≤1, a + b