1/1×2×3+1/2×3×4+1/3×4×5+1/4×5×6+1/5×6×71/1×2×3+1/2×3×4+1/3×4×5+1/4×5×6+1/5×6×7

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/06 14:50:33

1/1×2×3+1/2×3×4+1/3×4×5+1/4×5×6+1/5×6×71/1×2×3+1/2×3×4+1/3×4×5+1/4×5×6+1/5×6×7
1/1×2×3+1/2×3×4+1/3×4×5+1/4×5×6+1/5×6×7
1/1×2×3+1/2×3×4+1/3×4×5+1/4×5×6+1/5×6×7

1/1×2×3+1/2×3×4+1/3×4×5+1/4×5×6+1/5×6×71/1×2×3+1/2×3×4+1/3×4×5+1/4×5×6+1/5×6×7
1/2(1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5.-1/6*7)
=1/2(1/1*2-1/6*7)
=1/2(1/2-1/42)
=10/42

1/[n(n+1)(n+2)]=1/2*[1/n(n+1)-1/(n+1)(n+2)]
1/1×2×3+1/2×3×4+1/3×4×5+1/4×5×6+1/5×6×7
=1/2*[(1/1*2-1/2*3)+(1/2*3-1/3*4)+....+(1/5*6-1/6*7)]
=1/2*[1/1*2-1/6*7]
=1/2*(1/2-1/42)
=1/2*(21/42-1/42)
=1/2*20/42
=10/42

1/2(1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5。。。。-1/6*7)
=1/2(1/1*2-1/6*7)
=1/2(1/2-1/42)
=10/42