$~~~~\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+\frac{31}{32}+\frac{63}{64}+\frac{127}{128}+\frac{255}{256}$
$= 1-(\frac{1}{2})+(1- \frac{1}{4} )+(1- \frac{1}{8} )+···+ (1-\frac{1}{256})$
$=8-( \frac{1}{2} +\frac{1}{4}+\frac{1}{8}+···+\frac{1}{256})$
$=8-(1-\frac{1}{256} )$
$=8-1+ \frac{1}{256}$
$=7 \frac{1}{256}$
$~~~~\frac{1}{2}+\frac{1}{3}+\frac{2}{3}+\frac{1}{4}+\frac{2}{4}+\frac{3}{4}+\frac{1}{5}+\frac{2}{5}+···+\frac{1}{10}$
$~~~~+\frac{2}{10}+···+\frac{9}{10}$
$=0.5+1+1.5+2+···+4.5$
$=(0.5+4.5)×9÷2$
$=22.5$