Chapter 11 - Review - Page 668: 55

$S_{\infty}=10$

Using $S_{\infty}=\dfrac{a_1}{1-r}$, the sum of the infinite geometric sequence $ 5,\dfrac{5}{2},\dfrac{5}{4},... $ is \begin{array}{l} S_{\infty}=\dfrac{5}{1-\dfrac{1}{2}}\\\\ S_{\infty}=\dfrac{5}{\dfrac{1}{2}}\\\\ S_{\infty}=10 .\end{array}