用裂项法原式={2/(1*2)-2/(2*3)+2/(2*3)-2/(3*4)+.......-2/[(n+1)*(n+2)]}*(1/2) ={2/(1*2)-2/[(n+1)*(n+2)]}*(1/2) ={1-2/[(n+1)*(n+2)]}*(1/2) =1/2-1/[(n+1)(n+2)]