Dislocation subtraction is a common summation method of sequence, which is applied to the multiplication of geometric progression and arithmetic progression. As An=BnCn, where Bn is arithmetic progression and Cn is geometric progression; List Sn separately, and then multiply all formulas by the common ratio of geometric series at the same time, that is, kSn；; Then an error occurs, and the two are subtracted. For example, when x= 1, sn =1+3x+5x2+7x3+…+(2n-1) * x (n-1) (x ≠ 0), sn = 65438. When x is not equal to 1, sn =1+3x+5x2+7x3+…+(2n-1) * x (n-1); ∴xsn=x+3x^2； +5x^3； +7x^4+…+(2n- 1)*x^n； Subtract the two expressions to get (1-x) sn =1+2x [1+x+x 2; +x^3； +…+x^(n-2)]-(2n- 1)*x^n； Simplified to Sn = (2n-1) * x (n+1)-(2n+1) * x n+(1+x)/(1-x) 2sn = 65438. 21/2sn =1/4+1/8+...+1/2n+1(note that it is different from the original formula, so write it. In the question type: generally, it can only be used when the coefficient before a is equal to the index of a. This is an example (format problem, the numbers after a and n are exponents): s = a+2a2+3a3+…+(n-2) an-2+(n-1) an-1+nan (1) in (/) Equation (2) is as follows: as = a2+2a3+3a4+...+(n-2) an-1+(n-1) an+nan+1(2) with (1)- (1-a) s = a+A2+A3+...+ an-1+ an-nan+1. Finally, divide by (1-a) on both sides of the equation at the same time, and you can get the general formula of S. Example: sum sn = 3x+5x2; +7x^3； +...+(2n- 1) x's n-1power (x is not equal to 0) solution: when x= 1, sn =1+3+5+...+(2n-/kloc-0 When x is not equal to 1, sn = 3x+5x2; +7x^3； ; +...+(2n-1) x n-1power, so xsn = x+3 x2；; +5x^3； The fourth power of +7 ...+the n power of (2n-1) x, so (1-x) sn =1+2x (1+x+x 2; ; +x^3； ; N-2 power of +...+x)-(2n-1) N-power simplification of X: Sn = (2n- 1) x, n+ 1 power -(2n+ 1) x, N-power+(/) 8+7 *16+...+(2n-1) * 2n+(2n+1) * 2 (n+1) is subtracted to get -sn = 6+2 * 4+2 * 8. (4+8+16+...+2n)-(2n+1) * 2 (n+1) = 6+2 (n+2)-8-(2n+1) * 2. 8+...+1/2n+1/2 (n+1) (note that the position of the radical is different, so that it can be written more clearly) minus 1/2sn = 1/2-6558.