1/6+1/12+1/20+1/30+1/42+1/56+1/72等于多少?

发布网友发布时间：2024-10-16 03:01

共5个回答

热心网友时间：2024-10-18 04:32

1/6+1/12+1/20+1/30+1/42+1/56+1/72
=1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9
=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
=1/2-1/9
=7/18

热心网友时间：2024-10-18 04:25

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

1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9
=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
=1/2-1/9
=(9-2)/18
=7/18

热心网友时间：2024-10-18 04:32

1/6+1/12+1/20+1/30+1/42+1/56+1/72
=1/(2x3)+1/(3x4)+..+1/(8x9)

=(1/2-1/3)+(1/3-1/4)+..+(1/8-1/9)
=1/2-1/9
=7/18

热心网友时间：2024-10-18 04:32

用裂项法：
=1／2-1／9
=7／18

热心网友时间：2024-10-18 04:33

1/6+1/12+1/20+1/30+1/42+1/56+1/72
=(1/6+1/12)+(1/20+1/30)+1/42+1/56+1/72
=3/12+1/12+1/42+1/56+1/72
=1/3+1/42+1/56+1/72
=(1/3+1/42)+1/56+1/72
=5/14+1/56+1/72
=3/8+1/72
=7/18