math help

GP

a=1/3     r= 1/3     n=6

$$\\\boxed{S_n=\frac{a(1-r^n)}{1-r}}\\\\ S_6=\frac{\frac{1}{3}(1-(\frac{1}{3})^6)}{1-\frac{1}{3}}}\\\\ S_6=\frac{\frac{1}{3}(1-\frac{1}{3^6})}{\frac{2}{3}}}\\\\ S_6=\frac{1}{\not{3}}(1-\frac{1}{3^6})\times \frac{\not{3}}{2}\\\\ S_6=\frac{1}{2}(1-\frac{1}{3^6})\\\\$$

$${\mathtt{0.5}}{\mathtt{\,\times\,}}\left({\mathtt{1}}{\mathtt{\,-\,}}\left({\frac{{\mathtt{1}}}{{{\mathtt{3}}}^{{\mathtt{6}}}}}\right)\right) = {\frac{{\mathtt{364}}}{{\mathtt{729}}}} = {\mathtt{0.499\: \!314\: \!128\: \!943\: \!758\: \!6}}$$