观察每项得1/x-1/(x+1),将每一项进行拆分,前一项与后一项一部分相消,最后只剩1/x-1/(x+n),即为所求,具体这道题,解法如下：
1/1x2+1/2x3+1/3x4.1/1996x1997+1/1997x1998
=1-1/2+1/2-1/3+1/3-1/4+······+1/1997-1/1998
=1-1/1998
=1997/1998