Chapter 12 Sequences and Series - 12.4 Find Sums of Infinite Geometric Series - 12.4 Exercises - Skill Practice - Page 823: 17

$\dfrac{7}{10}$

Here, we have $a_n= a_1 r^{n-1}$ for the Geometric series. First term $a_1=1$ and Common ratio $r=\dfrac{-3}{7}$ The sum of an infinite Geometric Series can be found using: $S_n=\dfrac{a_1}{1-r}$ Thus, $S_n=\dfrac{1}{1-(\dfrac{-3}{7})}=\dfrac{1 \times 7}{7+3}$ Hence, $S_n=\dfrac{7}{10}$