1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72

来源：学生作业帮助网编辑：作业帮时间：2024/04/28 20:00:03

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72
1/2 = 1 - 1/2
1/6 = 1/2 - 1/3
1/12 = 1/3 - 1/4
依此类推
1/72 = 1/8 - 1/9
所以原式 = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +... + 1/8 - 1/9
= 1 - 1/9
= 8/9

原式=（1-1/2）+（1/2-1/3)+......+(1/8-1/9)
=1-1/2+1/2-1/3+......+1/8-1/9
=1-1/9
=8/9