1/1987*1988+1/1988*1989+1/1989*1990+.+1/1997*1998+1/1998*1999+1/1999

1/1987*1988+1/1988*1989+1/1989*1990+.+1/1997*1998+1/1998*1999+1/1999
1/1987*1988+1/1988*1989+1/1989*1990+.+1/1997*1998+1/1998*1999+1/1999

1/1987*1988+1/1988*1989+1/1989*1990+.+1/1997*1998+1/1998*1999+1/1999
1/(1987*1988)
=(1988-1987)/(1987*1988)
=1988/(1987*1988)-1987/(1987*1988)
=1/1987 - 1/1988
其余的几项也这样变形,最后,后面的项都正负相抵,剩下1/1987