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本文向高一同学介绍数列求和的常用方法. 1.错位相减例1 Sn=1+3x+5x2+7x3+…+ (2n-1)xn-1(x≠1) 分析由题可知,{(2n-1)xn-1}的通项是等差数列{2n-1}的通项与等比数列{xn-1}的通项之积,符合错位相减法的特征,可通过错位相减转化为等比数列的求和来解决. 设Sn=1+3x+5x2+7x3+…+ (2n-1)xn-1(x≠1) ①则xSn =x+3x2+5x3+7x4+…+(2n-1)xn ②由①-②,得
This article introduces the common methods of summation of numbers to high school students. 1. Displacement subtraction 1 Sn=1+3x+5x2+7x3+...+ (2n-1)xn-1(x≠1) The general term of (2n-1)xn-1} is the product of the general term of the {2n-1} series and the general term {xn-1} of the geometric series {Xn-1}, which is consistent with the characteristics of the misplaced subtraction method. Subtraction is converted to the sum of geometric progressions. Set Sn = 1 + 3x + 5x 2 + 7x 3 + ... + (2n - 1) xn - 1 (x 1) 1 then xSn = x + 3x 2 + 5x 3 + 7x 4 +... + (2n-1)xn 2 consists of 1-2,