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数列和函数有着密切的内在联系,数列是定义域为自然数集N或其子集上的一类特殊函数.特别地,等差数列的通项a_n是项数n的一次函数,其前n项和S_n=d/2n~2+(2a_1-d)/2n是n的二次函数;数列{(S_n/n)}是项数n的一次函数;等比数列的通项公式和前n项和公式也有着类似于指数函数式的结构特点.因此.在解决一些数列问题时,如果能从函数的思想出发,用函数的方法解题.将会有助于问题的解决和学生数学素质和思维能力的提高,增强学生分析问题和解决问题的能力.
The sequence has a close intrinsic relationship with the function. A sequence of numbers is a class of special functions whose domain is a set of natural numbers N or its subsets. In particular, the general term a_n of an arithmetic progression is a linear function of the number n of entries, the first n terms of which are. S_n=d/2n~2+(2a_1-d)/2n is a quadratic function of n; the sequence {(S_n/n)} is a linear function of the number n of terms; the general term formula of the geometric sequence and the first n terms The formulae also have structural features similar to those of the exponential function. Therefore, when solving some sequence problems, if we can proceed from the idea of the function, we can use the method of the function to solve the problem. It will be helpful for the solution of problems and the mathematical quality of students. Improve the ability of thinking, enhance students’ ability to analyze problems and solve problems.