1/2×3×4+1/3×4×5……1/19×20×21

1/2×3×4+1/3×4×5……1/19×20×21
1/2×3×4+1/3×4×5……1/19×20×21

1/2×3×4+1/3×4×5……1/19×20×21
1/2×3×4+1/3×4×5……1/19×20×21
=[1/(2×3)-1/(3×4)]×1/2+[1/(3×4)-1/(4×5)]×1/2+[1/(4×5)-1/(5×6)]×1/2+.+[1/(19×20)-1/(20×21)]×1/2
=1/2×[1/(2×3)-1/(3×4)+1/(3×4)-1/(4×5)+1/(4×5)-1/(5×6)+.+1/(19×20)-1/(20×21)]
=1/2×[1/(2×3)-1/(20×21)]
=1/2×（70/420-1/420）
=1/2×69/420
=69/840
=23/280

thank you very much!!!!