1/1×2×3×4+1/2×3×4×5+1/3×4×5×6+……+1/17×18×19×201/(1×2×3×4)+1/(2×3×4×5)+1/(3×4×5×6)+……+1/(17×18×19×20)

来源：学生作业帮助网编辑：作业帮时间：2024/05/09 02:29:09

1/1×2×3×4+1/2×3×4×5+1/3×4×5×6+……+1/17×18×19×201/(1×2×3×4)+1/(2×3×4×5)+1/(3×4×5×6)+……+1/(17×18×19×20)
1/1×2×3×4+1/2×3×4×5+1/3×4×5×6+……+1/17×18×19×20
1/(1×2×3×4)+1/(2×3×4×5)+1/(3×4×5×6)+……+1/(17×18×19×20)

1/1×2×3×4+1/2×3×4×5+1/3×4×5×6+……+1/17×18×19×201/(1×2×3×4)+1/(2×3×4×5)+1/(3×4×5×6)+……+1/(17×18×19×20)
原式=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+1/5*6*7-……+1/17*18*19-1/18*19*20)
=1/3*（1/1*2*3-1/18*19*20）
=1/3*1139/18*19*20
=1139/29754

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