Chapter 11 - Section 11.4 - Partial Sums of Arithmetic and Geometric Sequences - Exercise Set - Page 658: 22

$S_{\infty}=\dfrac{18}{5}$

Using $S_{\infty}=\dfrac{a_1}{1-r}$, the sum of the infinite geometric sequence $ 6,-4,\dfrac{8}{3},... $ is \begin{array}{l} S_{\infty}=\dfrac{6}{1-\left( -\dfrac{2}{3} \right)}\\\\ S_{\infty}=\dfrac{6}{\dfrac{5}{3}}\\\\ S_{\infty}=\dfrac{18}{5} .\end{array}