$\frac{3}{1×2}-\frac{5}{2×3}+\frac{7}{3×4}-\frac{9}{4×5}+\frac{11}{5×6}-\frac{13}{6×7}+\frac{15}{7×8}$
$=\frac{1+2}{1×2}-\frac{2+3}{2×3}+\frac{3+4}{3×4}-\frac{4+5}{4×5}+\frac{5+6}{5×6}-\frac{6+7}{6×7}+\frac{7+8}{7×8}$
$=(1+\frac{1}{2})-(\frac{1}{2}+\frac{1}{3})+(\frac{1}{3}+\frac{1}{4})-(\frac{1}{4}+\frac{1}{5})+(\frac{1}{5}+\frac{1}{6})-(\frac{1}{6}+\frac{1}{7})+(\frac{1}{7}+\frac{1}{8})$
$=1+\frac{1}{2}-\frac{1}{2}-\frac{1}{3}+\frac{1}{3}+\frac{1}{4}-\frac{1}{4}-\frac{1}{5}+\frac{1}{5}+\frac{1}{6}-\frac{1}{6}-\frac{1}{7}+\frac{1}{7}+\frac{1}{8}$
$=1+\frac{1}{8}$
$=1\frac{1}{8}$