1/2+1/6+1/20+1/30+1/42+1/56+1/72等于几?
来源:学生作业帮 编辑:搜搜考试网作业帮 分类:数学作业 时间:2024/08/18 02:43:28
1/2+1/6+1/20+1/30+1/42+1/56+1/72等于几?
![1/2+1/6+1/20+1/30+1/42+1/56+1/72等于几?](/uploads/image/z/125320-40-0.jpg?t=1%2F2%2B1%2F6%2B1%2F20%2B1%2F30%2B1%2F42%2B1%2F56%2B1%2F72%E7%AD%89%E4%BA%8E%E5%87%A0%3F)
1/2+1/6+1/20+1/30+1/42+1/56+1/72
=1/2+1/6+1/20+1/30+1/42+1/56+1/72+1/12-1/12
=1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72-1/12
=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+1/8-1/9-1/12
=1-1/9-1/12
=8/9-1/12
=32/36-3/36
=29/36
如果还有一个1/12的话
就是
1/2=1/(1*2)=1-1/2
1/6=1/(2*3)=1/2-1/3
1/12=1/(3*4)=1/3-1/4
1/20=1/(4*5)=1/4-1/5
1/30=1/(5*6)=1/5-1/6
1/42=1/(6*7)=1/6-1/7
1/56=1/(7*8)=1/7-1/8
1/72=1/(8*9)=1/8-1/9
原式=1-1/2+1/2-1/3+……+1/7-1/8+1/8-1/9=1-1/9=8/9
=1/2+1/6+1/20+1/30+1/42+1/56+1/72+1/12-1/12
=1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72-1/12
=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+1/8-1/9-1/12
=1-1/9-1/12
=8/9-1/12
=32/36-3/36
=29/36
如果还有一个1/12的话
就是
1/2=1/(1*2)=1-1/2
1/6=1/(2*3)=1/2-1/3
1/12=1/(3*4)=1/3-1/4
1/20=1/(4*5)=1/4-1/5
1/30=1/(5*6)=1/5-1/6
1/42=1/(6*7)=1/6-1/7
1/56=1/(7*8)=1/7-1/8
1/72=1/(8*9)=1/8-1/9
原式=1-1/2+1/2-1/3+……+1/7-1/8+1/8-1/9=1-1/9=8/9