数列可以说是一种特殊的函数,它可 以看做是自变量依次取正整数,图象为 一群孤立点的函数,所以在解有关数列 的问题时,应注重将其与函数有关的知 识结合在一起,注重函数与方程思想方 法的运用与渗透. 等差数列中,Sn=na1+n(n-1)/2d=d/2n2+ (a1-d/2)n.令A=d/2,B=a1-d/2,则Sn=An2+Bn. 当A≠0(即d≠0)时,Sn是关于n的二次式, A series of numbers can be said to be a special kind of function. It can be viewed as an independent variable that takes a positive integer in turn. The image is a function of a group of isolated points. Therefore, when solving a problem involving a series of numbers, it is important to combine the knowledge associated with the function. Together, pay attention to the application and penetration of function and equation methods. In the arithmetic sequence, Sn=na1+n(n-1)/2d=d/2n2+ (a1-d/2)n. Let A=d/2 ,B=a1-d/2, then Sn=An2+Bn. When A≠0 (ie, d≠0), Sn is a quadratic equation about n.