=1/4(1/1×2+1/2×3+1/3×4+……+1/1005×1006)
=1/4(1-1/2+1/2-1/3+1/3-1/4+……+1/1005-1/1006)
=1/4(1-1/1006)
=1005/4024
你的提取1/2是因为分母中的两个因素相差2