设1/2+1/3+1/4+...+1/1997=a,1/2+1/3+...+1/1996=b,则
原式=a(1+b)-(1+a)b
=a+ab-b-ab
=a-b
=1/2+1/3+1/4+...+1/1997-(1/2+1/3+...+1/1996)
=1/1997