1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=（1-1/2）+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/9-1/10)
=1-1/10
=9/10

1/2=1/1-1/2
1/6=1/2-1/3
1/12=1/3-1/4
...
1/90=1/9-1/10
所以1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=1/1-1/10=9/10

=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)+(1/8-1/9)+(1/9-1/10)=9/10