将分子拆开如1/1×2=1-1/2；1/2×3=1/6=1/2-1/3；1/3×4=1/12=1/3-1/4.以此类推1/1×2+1/2×3+••••••+1/9×10=1-1/2+1/2-1/3+1/3-1/4+.1/8-1/9+1/9-1/10=1-1/10=9/10...