1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1(x+2009)(x+2010)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+...+1/(x+2009)-1/(x+2010)
=1/x-1/(x+2010)
故当x=1时,原式=1 -1/2011 =2010/2011