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多项分数和问题是初中数学竞赛中的重要内容,在近几年全国各地数学竞赛中经常出现.在多项分数求和问题中,将其中一些分数拆开,使得拆开后的一些分数可以互相抵消,从而达到简化运算的目的,这种方法称之为裂项抵消法.本文以近几年各地竞赛试题为例,重点介绍裂项抵消法,供读者参考.1.直接裂项如果多项分数和式中的每一项易于分拆,可以利用裂项抵消法求和.例1(2009年北京市中学生数学竞赛)
Many scores and problems are important parts of the junior high school math competition, which have been frequently seen in mathematics contests throughout the country in recent years.Owing the scores of multiple points, some of these scores are taken apart, Offset each other, so as to achieve the purpose of simplifying computing, this method is called the fissure offsetting method.In this paper, the contest questions in recent years as an example, with emphasis on fissure offsetting method for readers to reference.1 direct fission if a number Each of the scores and the formulas is easy to split and can be summed using the fission offset method Example 1 (2009 Beijing Junior High School Students Mathematical Contest)