数列的实质是函数,用函数思想解数列问题能够加深对数列概念及公式的理解,加强知识点间的联系,增强化归能力.1　利用一次函数性质例1　设ｓｎ为等差数列{ａｎ}的前ｎ项和,求证:ｓｍ+ｎｍ+ｎ=ｓｍ-ｓｎｍ-ｎ.证　设{ａｎ}公差为ｄ,则ｓｎ=ｎａ1+ｎ(ｎ-1)2ｄ.∴ｓｎｎ=ｄ2ｎ... The essence of a sequence is a function. Using a function to solve a sequence problem can deepen the understanding of the sequence concept and formula, strengthen the connection between the knowledge points, and enhance the ability to transform. 1. Use the properties of a single function. Example 1 Let sn be an arithmetic sequence {an} The first n terms of the sum, verification: sm + nm + n = sm-snm-n. Prove that {an} tolerance d, then sn = na1 + n (n-1) 2d. ∴ snn = d2n ...