x/ab+x/(a+1)(b+1)+x/(a+2)(b+2)+...+x/(a+2011)(b+2011)
=x-x/2+x/2-x/3+x/3-x/4+……+x/2012-x/2013
=x-x/2013
=2012x/2013=2012
所以x=2013