请写清楚,

原式=(1/2)×{2/[(x(x+2)]+2/[(x+2)(x+4)]+2/(x+4)(x+6)+……+2/[(x+2010)(x+2012)]}=(1/2)×{[(1/x)-1/(x+2)]+[1/(x+2)-1/(x+4)]+[1/(x+4)-1/(x+6)]+……+[1/(x+2010)-1/(x+2012)]}=(1/2)×[(1/x)-1/(x+2)+1/(x+2)-1/(x+4)+1/(x+4)-1/(x+6)+……+1/(x+2010)-1/(x+2012)]=(1/2)×[(1/x)-1/(x+2012)]=(1/2)×{(x+2012)/[x(x+2012)]-x/[x(x+2010)]}=(1/2)×(x+2012-x)/[x(x+2012)]=(1/2)×(2012)/[x(x+2012)]=1006/[x(x+2012)]