Đáp án:
`x=2008`
Giải thích các bước giải:
`1/3+1/6+1/10+...+2/(x(x+1))=2007/2009`
`=>1/2(1/3+1/6+1/10+...+2/(x(x+1)))=1/2. 2007/2009`
`=>1/6+1/12+1/20+...+1/(x(x+1))=2007/4018`
`=>1/2.3+1/3.4+1/4.5+...+1/(x(x+1))=2007/4018`
`=>1/2-1/3+1/3-1/4+1/4-1/5+...+1/x-1/(x+1)=2007/4018`
`=>1/2-1/(x+1)=2007/4018`
`=>1/(x+1)=1/2-2007/4018=2/4018=1/2009`
`=>x+1=2009`
`x=2008`
Vậy `x=2008`
