Answer
$S=2,391,484.33333...$
Work Step by Step
Write the sum in the form: $\displaystyle \sum_{k=1}^{n}a_{1}r^{k-1}$
$\displaystyle \frac{3}{9}+\frac{3^{2}}{9}+\frac{3^{3}}{9}+\dots+\frac{3^{15}}{9}=$
$=\displaystyle \frac{3}{9}(3^{0})+\frac{3}{9}(3^{1})+\frac{3}{9}(3^{2})+\dots +\frac{3}{9}(3^{14})$
$=\displaystyle \sum_{n=1}^{15}\frac{1}{3}(3^{k-1})$
Using the calculator at desmos.com,
$S=2,391,484.33333$
