1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6+...+1/8x9x10 =1-1/2-1/2(1-1/3)+1/2-1/3-1/2(1/2-1/4)+1/3-1/4-1/2(1/3-1/5)+1/4-1/5-1/2(1/4-1/6)+.+1/8-1/9-1/2(1/8-1/10)=1-1/9-1/2(1+1/2-1/9-1/10)=173/360