1/1×2×3+1/2×3×4+、、、+1/20×21×22=?

1/1×2×3=（1/1×2-1/2×3）×1/2
1/2×3×4=（1/2×3-1/3×4）×1/2
……
1/20×21×22=（1/20×21-1/21×22）×1/2
1/1×2×3+1/2×3×4+、、、+1/20×21×22
=（1/1×2-1/2×3）×1/2+（1/2×3-1/3×4）×1/2+……
+（1/20×21-1/21×22）×1/2
=(1/2)×(1/1×2-1/21×22)
=115/462