1/1*3+1/2*4+1/3*5+1/4*6+1/5*71+/6*8+1/7*9+1/8*10=?
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/24 00:36:35
![1/1*3+1/2*4+1/3*5+1/4*6+1/5*71+/6*8+1/7*9+1/8*10=?](/uploads/image/z/6881509-37-9.jpg?t=1%2F1%2A3%2B1%2F2%2A4%2B1%2F3%2A5%2B1%2F4%2A6%2B1%2F5%2A71%2B%2F6%2A8%2B1%2F7%2A9%2B1%2F8%2A10%3D%3F)
1/1*3+1/2*4+1/3*5+1/4*6+1/5*71+/6*8+1/7*9+1/8*10=?
1/1*3+1/2*4+1/3*5+1/4*6+1/5*71+/6*8+1/7*9+1/8*10=?
1/1*3+1/2*4+1/3*5+1/4*6+1/5*71+/6*8+1/7*9+1/8*10=?
=1/2*【(1-1/3)+(1/2-1/4)+(1/3-1/5)+.+(1/8-1/10)】
=1/2*(1+1/2-1/9-1/10)
=1/2*(3/2-19/90)
=1/2*(116/90)
=29/45
原式=1/(1*3)+1/(3*5)+1/(5*7)+1/(7*9)+1/(2*4)+1/(4*6)+1/(6*8)+1/(8*10)
=(1/2)*(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9)+(1/2)*(1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10)
=(1/2)*(1-1/9+1/2-1/10)
=(1/2)*(58/45)
=29/45