由于【（x+1）-x】/x(x+1) =1/x(x+1)所以1/x(x+1)=1/x-1/(x+1)同理可得：1/(x+1)(x+2)=1/(x+1)-1/(x+2)·····所以原方程可写为：【1/x-1/(x+1)】+【1/(x+1)-1/(x+2)】+····【1/(x+8)-1/(x+9)】=2x+3/x(x+9)...