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