1/2*1/3+1/3*1/4+1/4*1/5+1/5*1/6+1/6*1/7+1/7*1/8+1/8*1/9
=1/3(1/2+1/4)+1/5(1/4+1/6)+1/7(1/6+1/8)+1/8*1/9
=1/4+1/12+1/24+1/72
=1/4(1+1/3)+1/24(1+1/3)
=1/3+1/3*1/6=1/3*(1+1/6)=7/18不好意思,请问为什么要这样算奇数的公倍数少,把奇数的分数提出来,剩下的都是偶数,能找到公倍数,可以进一步简化,实际我还是懒了些,可以这样进一步简化有公约数的乘法最简便=1/3(1/2+1/4)+1/5(1/4+1/6)+1/7(1/6+1/8)+1/8*1/9=1/3*1/2(1+1/2)+1/5*1/2(1/2+1/3)+1/7*1/2(1/3+1/4)+1/2*1/4*1/9=1/2*1/2+1/2*1/6+1/2*1/12+1/2*1/36=1/2*1/2(1+1/3)+1/2*1/12(1+1/3)=1/3+1/18=1/3(1+1/6)=7/18