用定积分定义求一类和式和极限

Seeking the Limit of a Sum by the Definition of Definite Integral

和式极限是一个基本的数学问题,由于解法的多样性,也是一个难题。讨论一类用定积分定义求和式极限的方法,同时这种方法充分表现了和式极限与积分这两个不同的数学概念之间的紧密联系,也表现出求和式极限的多样性与灵活性。

The limit of a sum is a basic mathematic problem, and for the solution＇s diversity, it is a difficult problem too. This paper discusses a method to seek the limit of a sum by one kind of definite integral＇s definition. this method represents the close relation between two different mathematic concepto——the limit of a sum and definite integral sufficiently, and represents the diversity and flexibility of seeking the limit of a sum.