1/(1×3)+1/(3×5)+1/(5×7)+…………+1/(1997×1999）
=1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+……+1/2(1/1997-1/1999)
=1/2(1-1/3+1/3-1/5+1/5-1/7+……-1/1997+1/1997-1/1999)
=1/2(1-1/1999)
=999/1999