$\begin{align}  & a=0.5,\text{  }r=\frac{0.05}{0.5}=0.1 \\ & {{S}_{\infty }}=\frac{a}{1-r}=\frac{0.5}{1-0.1}=\frac{0.5}{0.9}=\frac{5}{9} \\\end{align}$