Question

1/6=1/2-1/3，1/12=1/3-1/4，1/20=1/4-1/5，根据以上规律计算下题。1/6+1/12+1/20+1/30+1/42+1/56+1/72

1/6=1/2-1/3，1/12=1/3-1/4，1/20=1/4-1/5，根据以上规律计算下题。1/6+1/12+1/20+1/30+1/42+1/56+1/72

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

原式=
(1/2-1/3)+(1/3-1/4)+(1/4+1/5)+……+(1/8-1/9)
=1/2-1/3+1/3-1/4+1/4+1/5+……+1/8-1/9
=1/2-1/9
=7/18