3 sum Sn = 1 (1 / 3) + 3 (1 / 3) ^ 2 + 5 (1 / 3) ^ 3 + +(2n-1) (1 / 3) ^ n (I used the method of dislocation subtraction for a long time, but I can't solve it later

3 sum Sn = 1 (1 / 3) + 3 (1 / 3) ^ 2 + 5 (1 / 3) ^ 3 + +(2n-1) (1 / 3) ^ n (I used the method of dislocation subtraction for a long time, but I can't solve it later

Sn=1(1/3)+3(1/3)^2+5(1/3)^3+…… +(2n-1)(1/3)^n 3Sn=1+3*(1/3)+5*(1/3)^2+.+(2n-1)*(1/3)^(n-1)3Sn-Sn=1+2*(1/3)+2*(1/3)^2+...+2*(1/3)^(n-1)-(2n-1)*(1/3)^n2Sn=1+2*(1/3)*[1-(1/3)^(n-1)]/(1-1/3)-(2n-1)*(...