1/3+1/18+1/54+1/108+.+1/378=1/3+1/(3*6)+...+1/(18*21)=1/3 + (1/3)*[(6-3)/(3*6)+(9-6)/(6*9)+...+(21-18)/(18*21)]=1/3*[1+(1/3-1/6+1/6-1/9+...+1/18-1/21)=1/3*[1+1/3-1/21]=3/7≈0.43