Answer
$S=4.99858944505$
Work Step by Step
Write the sum in the form: $\displaystyle \sum_{k=1}^{n}a_{1}r^{k-1}$
$S=2+\displaystyle \frac{6}{5}+\frac{18}{25}+\cdots+2\left(\frac{3}{5}\right)^{15}=$
$=2\displaystyle \left(\frac{3}{5}\right)^{0}+2\left(\frac{3}{5}\right)^{1}+...+2\left(\frac{3}{5}\right)^{15}$
$S=\displaystyle \sum_{n=1}^{16}(2)(\frac{3}{5})^{n-1}$
Using the calculator at desmos.com,
$S=4.99858944505$
