原方程可化为:(1/2)[1/x-1/(x+1)]+(1/2)[1/(x+2)-1/(x+4)]+…+(1/2)[1/(x+8)-1/(x+10)]=5/241/x-1/(x+10)=5/1212(x+10)-12x=5x(x+10)x²+10x-24=0(x-2)(x+12)=0x=2或x=-12