Đáp án:
`1/(1.2.3)+1/(2.3.4)+..........+1/(98.99.100)`
Đặt `A=1/(1.2.3)+1/(2.3.4)+..........+1/(98.99.100)`
`2A= 2/(1.2.3)+2/(2.3.4)+.........+2/(98.99.100)`
Mà `2/(1.2.3)=1/(1.2)-1/(2.3)`
`2/(2.3.4)=1/(2.3)-1/(3.4)`
...............................................................
`2/(98.99.100)=1/(98.99)-1/(99.100)`
---> `2A=1/(1.2)-1(2.3) +1/(2.3)-1/(3.4)+..................+1/(98.99)-1/(99.100)`
`2A=1/(1.2)-1/(99.100)`
`2A=1/2 - 1/9900`
`2A=4950/9900 - 1/9900`
`2A= 4949/9900`
--> `A= 4949/9900 : 2 =4949/19800`
XIN HAY NHẤT NHA
@hoang
