=[2/x(x+2) +2/(x+2)(x+4) +2/(x+4)(x+6)+...+2/(x+2010)(x+2012)]/2
=[1/x-1/(x+2)+1/(x+2)-1/(x+4)+1/(x+4)-……-1/(x+2010)+1/(x+2010)-1/(x+2012)]/2
=[1/x-1/(x+2012)]/2
=1006/x(x+2012)
如:2/(x+4)(x+6)=[(x+6)-(x+4)]/(x+4)(x+6)=(x+6)/(x+4)(x+6)-(x+4)/(x+4)(x+6)=1/(x+4)-1/(x+6)