依题意得
Sn=1+3S+5S^2+7S^3+···+(2n-1)S^(n-1) ①
等式两边同乘以S,则
SSn=1S+3S^2+5S^3+7S^4+···+(2n-1)S^n ②
则由①-②得
(1-S)Sn=1+2S+2S^2+2S^3+···+2S^(n-1)-(2n-1)S^n
即(1-S)Sn=﹛2S[1-S^(n-1)]/(1-S)﹜+1-(2n-1)S^n
则Sn=﹛2S[1-S^(n-1)]/(1-S)^2﹜+[1-(2n-1)S^n]/(1-S)