1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90 这道数学题的简便运算怎么解小学题目

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90 这道数学题的简便运算怎么解小学题目
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90 这道数学题的简便运算怎么解
小学题目

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90 这道数学题的简便运算怎么解小学题目
2化成1*2
6化成2*3
以此类推
1／2写成1-1／2
1／6写成1／2-1／3
以此类推就可以约去
最后答案9／10

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

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

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*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)
=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
=1-1/10
=9/10