1/1乘2乘3乘4+1/2乘3乘4乘5+1/3乘4乘5乘6+.+1/17乘18乘19乘20

1/(1×2×3×4)+1/(2×3×4×5)+1/(3×4×5×6)+……+1/(17×18×19×20)=1/3×(1/1×2×3-1/2×3×4+1/2×3×4-1/3×4×5+1/3×4×5-1/4×5×6+1/4×5×6-……+1/17×18×19-1/18×19×20)=1/3×（1/1×2×3-1/18×19×20）=1/3×1139/18×19×20=1139/20520