=1/4(1/1×2+1/2×3+1/3×4+……+1/1006×1007)
=1/4(1-1/2+1/2-1/3+1/3-1/4+……+1/1006-1/1007)
=1/4(1-1/1007)
=1/4×1006/1007
=503/2104