Question

数学问题解决

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

Answer 1

1/2 = 1 - 1/2
1/6 = 1/2 - 1/3
1/12 = 1/3 - 1/4
依此类推
1/72 = 1/8 - 1/9

所以原式 = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +... + 1/8 - 1/9
= 1 - 1/9
= 8/9

Answer 2

8/9

Answer 3

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

Answer 4

原式=1/(1乘2)+1/(2乘3)+1/(3乘4)+1/(4乘5)+1/(5乘6)+1/(6乘7)+1/(7乘8)+1/(8乘9)=(1-1/2)+(1/2-1/3)+(1/3-1/4)+ +(1/8-1/9)=1-1/9=8/9