1+ 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729
=1093/729
A=1+1/3+1/3^2+......1/3^6
3A= 3 +1 + 1/3+......=1/3^5
3A-A= 3-1/3^6
A=\(\frac{3-\frac{1}{3^6}}{2}\)
\(A=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)
\(A\)\(x\)\(3=3x\left(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\right)\)
\(A\)\(x3=3+1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)
\(A\)\(x3=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+3\)
\(-A=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)
\(A\)\(x2=3-\frac{1}{729}=\frac{2186}{729}\)
\(A=\frac{2186}{729}:2=\frac{1093}{729}\)
