Answer
$\$32767$.
Work Step by Step
From the given information, we can observe that it is a geometric series
$1,2,4\cdots $
Here ${{a}_{1}}=1$ and common ratio $r=2$ and $n=15$.
Using the formula for the sum of a geometric series, we can find the sum of finite terms ${{S}_{n}}=\frac{{{a}_{1}}\left( 1-{{r}^{n}} \right)}{\left( 1-r \right)}$.
So;
$\begin{align}
& {{S}_{n}}=\frac{1\left( 1-{{2}^{15}} \right)}{\left( 1-2 \right)} \\
& =\frac{1\left( 1-32768 \right)}{-\left( 1 \right)} \\
& =32767
\end{align}$
