Sum by dislocation subtraction: sum: SN = 1 + 3x + 5x2 + 7X3 + +（2n-1）xn-1．

Sum by dislocation subtraction: sum: SN = 1 + 3x + 5x2 + 7X3 + +（2n-1）xn-1．

It can be seen from the question that the general term of {(2n-1) XN-1} is the product of the general term of the arithmetic sequence {2N-1} and the general term of the proportional sequence {XN-1} +（2n-1）xn-1，∴xSn＝x+3x2+… +(2n − 3) xn − 1 + (2n-1) xn, the subtraction of the two formulas gives (1-x) Sn = 1 + 2x + 2x2 + +2xn-1 - (2n-1) xn, ① when x ≠ 1,0, from the summation formula of the equal ratio sequence, we can get: (1-x) Sn = - 1 + 2 (1 − xn) 1 − X - (2n-1) xn, ｜ Sn = (2n − 1) xn + 1 − (2n + 1) xn + (1 + x) (1 − x) 2; ② when x = 1, Sn = 1 + 3 + 5 + +(2n-1) = n (1 + 2n − 1) 2 = N2. ③ when x = 0, Sn = 1 + 0 = 1