+118609 GP
a=1/3 r= 1/3 n=6
$$\\\boxed{S_n=\frac{a(1-r^n)}{1-r}}\\\\
S_6=\frac{\frac{1}{3}(1-(\frac{1}{3})^6)}{1-\frac{1}{3}}}\\\\
S_6=\frac{\frac{1}{3}(1-\frac{1}{3^6})}{\frac{2}{3}}}\\\\
S_6=\frac{1}{\not{3}}(1-\frac{1}{3^6})\times \frac{\not{3}}{2}\\\\
S_6=\frac{1}{2}(1-\frac{1}{3^6})\\\\$$
$${\mathtt{0.5}}{\mathtt{\,\times\,}}\left({\mathtt{1}}{\mathtt{\,-\,}}\left({\frac{{\mathtt{1}}}{{{\mathtt{3}}}^{{\mathtt{6}}}}}\right)\right) = {\frac{{\mathtt{364}}}{{\mathtt{729}}}} = {\mathtt{0.499\: \!314\: \!128\: \!943\: \!758\: \!6}}$$
+118609 GP
a=1/3 r= 1/3 n=6
$$\\\boxed{S_n=\frac{a(1-r^n)}{1-r}}\\\\
S_6=\frac{\frac{1}{3}(1-(\frac{1}{3})^6)}{1-\frac{1}{3}}}\\\\
S_6=\frac{\frac{1}{3}(1-\frac{1}{3^6})}{\frac{2}{3}}}\\\\
S_6=\frac{1}{\not{3}}(1-\frac{1}{3^6})\times \frac{\not{3}}{2}\\\\
S_6=\frac{1}{2}(1-\frac{1}{3^6})\\\\$$
$${\mathtt{0.5}}{\mathtt{\,\times\,}}\left({\mathtt{1}}{\mathtt{\,-\,}}\left({\frac{{\mathtt{1}}}{{{\mathtt{3}}}^{{\mathtt{6}}}}}\right)\right) = {\frac{{\mathtt{364}}}{{\mathtt{729}}}} = {\mathtt{0.499\: \!314\: \!128\: \!943\: \!758\: \!6}}$$
