Consider the following.

${\displaystyle \underset{n=1}{\overset{}{}}}2(0\mathrm{.}9{)}^{n-1}$

$($a$)$ Find the.sum.of$.$the series.

$S_n=$

Enter an exact number.

$($b$)$ Use a graphing utility to find the indicated partial sum and complete the table. $($Round your answers to four decimal places.$)$

$($c$)$ Use a graphing utility to graph the first $10$ terms of the sequence of partial sums and a horizontal line representing the sum.