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

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

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

7/8

1/2+1/6+1/12+1/20+1/30+1/42+1/56
=1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7/8
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1-1/8
=7/8
关键是运用公式1/(n-1)n= 1/(n-1)-1/n

答案7/8

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

1/2+1/6+1/12+1/20+1/30+1/42+1/56
=1/2+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+（1/5-1/6)+（1/6-1/7）+(1/7-1/8)
=1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1-1/8
=7/8

1/2+1/6+1/12+1/20+1/30+1/42+1/56
=1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7/8
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1-1/8
=7/8
给你个公式自己去套套
1/(n-1)n= 1/(n-1)-1/n

1/1*1/2+1/2*1/3+1/3*1/4+....+1/n*1/(n+1)=1/1-1/2+1/2-1/3+1/3-1/4+....+1/n-1/(n+1)=1-1/(n+1)
上式等于1-1/8=7/8