$1/1.2 + 1/2.3 + 1/3.4 + ... + 1/x(x+1) = 2008/2009$
$1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/x - 1/x+1 = 2008/2009$
$1 - 1/x+1 = 2008/2009$
$1 - 1/x+1 = 2008/2009$
$1/x+1 = 1 - 2008/2009$
$1/x+1 = 1/2009$
$⇒ x+1 = 2009$
$⇒ x = 2008$
Vậy $x = 2008.$
HỌC TỐT!