\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{18}+\frac{1}{54}+\frac{1}{162}\)
\(A=\frac{81}{162}+\frac{27}{162}+\frac{9}{162}+\frac{3}{162}+\frac{1}{162}\)
\(A=\frac{\left(81+9\right)+\left(27+3\right)+1}{162}\)
\(A=\frac{90+30+1}{162}\)
\(A=\frac{121}{162}\)
\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{18}+\frac{1}{54}+\frac{1}{162}\)
\(3A=\frac{3}{2}+\frac{1}{2}+\frac{1}{6}+\frac{1}{18}+\frac{1}{54}\)
\(2A=\frac{3}{2}-\frac{1}{162}\)
\(A=\frac{121}{162}\)