Đáp án:
`x=4017`
Giải thích các bước giải:
`2/(2.3)+2/(3.4)+....+2/(x(x+1))=2008/2009(x ne 0,-1)`
`=>1/(2.3)+1/(3.4)+....+1/(x(x+1))=1004/2009`
`=>1/2-1/3+1/3-1/4+.....+1/x-1/(x+1)=1004/2009`
`=>1/2-1/(x+1)=1004/2009`
`=>(x+1-2)/(2x+2)=1004/2009`
`=>(x-1)/(2x+2)=1004/2009`
`=>2009(x-1)=1004(2x+2)`
`=>2009x-2009=2008x+2008`
`=>x=2008+2009`
`=>x=4017`
Vậy `x=4017`