sn=1+3a+5a^2+7a^3+ .+(2n-1)a^n-1 ①
a*sn= a+3a^2+5a^3+ .+(2n-3)a^n-1+(2n-1)a^n ②
①式－②式：（1-a)sn=1+2a+2a^2+2a^3+.+2a^(n-1)-(2n-1)a^n
=-1+[2+2a+2a^2+2a^3+.+2a^(n-1)]-(2n-1)a^n
=-1+[2*(1-a^n)/1-a]-(2n-1)a^n
=[1+a-(2n+1)*a^n+(2n-1)*a^n+1]/(1-a)
sn=[1+a-(2n+1)*a^n+(2n-1)*a^n+1]/(1-a)^2