Chapter 12 Sequences and Series - 12.4 Find Sums of Infinite Geometric Series - 12.4 Exercises - Skill Practice - Page 823: 23

$18$

Here, we have $a_n= a_1 r^{n-1}$ for the Geometric series. First term $a_1=3$ and Common ratio $r=\dfrac{5}{6}$ The sum of an infinite Geometric Series can be found using: $S_n=\dfrac{a_1}{1-r}$ Thus, $S_n=\dfrac{3}{1-(\dfrac{5}{6})}=\dfrac{18}{6-5}$ Hence, $S_n=18$