${\displaystyle \underset{n=1}{\overset{}{}}}3(0\mathrm{.}8{)}^{n-1}$

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

$S_n=$

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

$\backslash$table$[[n,5,10,20,50,100],[S_n,,,,,]]$

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