3求和 Sn=1（1/3）+3（1/3）^2+5(1/3)^3+……+(2n-1)(1/3)^n (这个题我用错位相减法做了半天后来不会解了

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)*(...给Sn乘以1/3该怎么做呢Sn=1（1/3）+3（1/3）^2+5(1/3)^3+……+(2n-1)(1/3)^n (1/3)Sn=1*(1/3)^2+3*(1/3)^3+5*(1/3)^4+.....+(2n-1)*(1/3)^(n+1)Sn-(1/3)Sn=1*(1/3)+2*(1/3)^2+2*(1/3)^3+...+2*(1/3)^n-(2n-1)*(1/3)^(n+1)(2/3)Sn=-(1/3)+2*(1/3)+2*(1/3)^2+2*(1/3)^3+...+2*(1/3)^n-(2n-1)*(1/3)^(n+1)=-1/3+2*(1/3)*[1-(1/3)^n]/(1-1/3)-(2n-1)*(1/3)^(n+1)=-1/3+1-(1/3)^n-(2n-1)*(1/3)^(n+1)=2/3-3*(1/3)^(n+1)-(2n-1)*(1/3)^(n+1)=2/3-(2n+2)*(1/3)^(n+1)Sn=1-(n+1)*(1/3)^n