1/1×3=(1-1/3)/2
1/3×5=(1/3-1/5)/2
1/5×7=(1/5-1/7)/2
.
.
1/9×11=(1/9-1/11)/2
2002/1×3+2002/3×5+2002/5×7+2002/7×9+2002/9×11
=2002×1/2×(1/1×3+1/3×5+1/5×7+1/7×9+1/9×11)
=2002×1/2×(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)
=2002×1/2×(1-1/11)
=2002×1/2×10/11
=910