1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=1怎么算简便?

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=1怎么算简便?
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=1怎么算简便?

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=1怎么算简便?
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+……1/9-1/10 （除了1与1/10,两两抵消）
＝1-1/10
＝9/10
呵呵,加油!不懂再问,诚答!

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

（1-1/2)+(1/2-1/3)+(1/3_1/4)...+(1/9-1/10)= 1-1/10 自己看 你题目有问题

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+……+1/10*11
=(1/1-1/2)+(1/2-1/3)+……+(1/10)
=1

注意观察分母
1/2=1/(1*2)=1-1/2
1/6=1/(2*3)=1/2-1/3
.....
1/[n*(n+1)]=1/n-1/(n+1)
所以原式=1-1/2+1/2-1/3+1/3-1/4+.....-1/10=9/10
你的答案错了

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+……1/9-1/10
除了开始的1和最后的1/10 其余的都相互销了
最后用1-1/10 =9/10