3/1×5+3/5×9+3/9×13+……+3/1997×2001
=3×4×﹙1/1-1/5+1/5-1/9+1/9-1/13+……+1/1997-1/2001﹚
=12×﹙1-1/2001﹚
=12×2000/2001
=8000/667.