Đáp án:
`x=2008`
Giải thích các bước giải:
`1/3 + 1/6 + 1/10 + ... + 2/(x(x+1)) = 2007/2009`
`to 2/6 + 2/12 + 2/20 + ... + 2/(x(x+1)) = 2007/2009`
`to 2 . ( 1/6 + 1/12 + 1/20 + ... + 1/(x(x+1)) ) = 2007/2009`
`to 2 . ( 1/2.3 + 1/3.4 + 1/4.5 + ... + 1/(x(x+1)) ) = 2007/2009`
`to 2 . ( 1/2-1/3+1/3-1/4+1/4-1/5+...+1/x-1/(x+1) ) = 2007/2009`
`to 1/2 - 1/(x+1) = 2007/2009 : 2`
`to (x+1-2)/(2(x+1)) = 2007/4018`
`to (x-1)/(2x+2) = 2007/4018`
`to 4018.(x-1) = 2007.(2x+2)`
`to 4018x-4018 = 4014x+4014`
`to 4018x-4014x = 4014+4018`
`to 4x = 8032`
`to x=2008`
Vậy `x=2008`
