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数列是一类特殊的函数,我们常用函数观点把等差数列中的数量关系表示出来加以研究,这种利用函数思想合理转化的手段是解决等差数列问题的重要策略。如研究等差数列的通项公式及前n项和公式时,应与一元一次、一元二次函数联系起来。等差数列与函数的交汇问题常见的有两种类型:一种是以函数为载体考查等差数列的有关运算;另一种是以构造函数解决等差数列的最值问题。
The sequence is a kind of special function, and we often use the viewpoint of function to show the relationship between the numbers in arithmetic progression. The means of rational transformation using function thought is an important strategy to solve the problem of arithmetic progression. For example, when studying the general formula and the first n terms and formulas of the arithmetic progression of differential equations, it should be connected with a one-time, one-quadratic function. There are two kinds of common problems in the intersection of arithmetic progression and function: one is to use the function as a carrier to examine the arithmetic of arithmetic progression, and the other is to solve the most value problem of arithmetic progression with constructor.