$=\frac{3}{2}+\frac{9}{4}+\frac{25}{8}+\frac{65}{16}+\frac{161}{32}$
$=1\frac{1}{2}+2\frac{1}{4}+3\frac{1}{8}+4\frac{1}{16}+5\frac{1}{32}$
$=(1+2+3+4+5)+(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32})$
$=15+(1-\frac{1}{32})$
$=15\frac{31}{32}$
