一题找规律的数学题（初三）

1/2 =1/(1*2)
1/6 =1/(2*3)
1/12 =1/(3*4)
1/20 =1/(4*5)
1/30 =1/(5*6)

因为1/(n乘n+1)=1/n-1/(n+1) 你自己化简一下就知道
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110

= 1/(1*2)+1/(2*3)+1/(3*4)+...+1/(9*10) +1/(10*11)

= (1/1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/9-1/10)+(1/10-1/11)

=1-1/11

=10/11

祝你学习天天向上，加油！！！！！！！！！

(1/1*2)+(1/2*3)+( 1/3*4)+··(1/10*11)
=1-1/2+1/2-1/3+1/3-1/4+···+1/9-1/10+1/10-1/11
=1-1/11
=10/11

1/2=1-1/2 ，1/6=1/2-1/3， 1/12=1/3-1/4，1/20=1/4-1/5……
所以1/2+1/6+1/12+1/20+……
=1-1/2+1/2-1/3+1/3-1/4+……+1/10-1/11
=1-1/11
=10/11
我是中学教师，就这样做