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