因为1/[x(x+1)]=1/x-1/(x+1)
同理1/[(x+1)(x+2)]=1/(x+1)-1/(x+2 )
1/(x+2)(x+3)=1/(x+2)-1/(x+3)
整理得2/x-1/(x+3)+2=0
去分母得2x^2+7x+6=0
x=-1.5 x=-2(舍去）