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+（1/2-1/3）+（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）

=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

=1-1/10

=9/10

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+1/90
=4/6+1/3*1/4+1/4*1/5+1/5*1/6+1/6*1/7+1/7*1/8+1/90
=1/3*6+1/5*（1/4+1/6）+1/7*（1/6+1/8）+1/90
=1/3*6+1/5*10/24+1/7*14/48+1/90
=1/18+1/12+1/24+1/90
=1/6*（1/3+1/2+1/4）+1/90
=1/6*（5/6+1/4）+1/90
=1/6*13/10+1/90
=1/30*（13/2+1/3）
=1/30*（39/6+2/6）
=1/30*41/6
=41/90本回答被网友采纳

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