1/1×2×3+1/2×3×4+、、、+1/20×21×22=?请光速回答!
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/21 09:45:39
![1/1×2×3+1/2×3×4+、、、+1/20×21×22=?请光速回答!](/uploads/image/z/395949-21-9.jpg?t=1%2F1%C3%972%C3%973%2B1%2F2%C3%973%C3%974%2B%E3%80%81%E3%80%81%E3%80%81%2B1%2F20%C3%9721%C3%9722%3D%3F%E8%AF%B7%E5%85%89%E9%80%9F%E5%9B%9E%E7%AD%94%21)
1/1×2×3+1/2×3×4+、、、+1/20×21×22=?请光速回答!
1/1×2×3+1/2×3×4+、、、+1/20×21×22=?
请光速回答!
1/1×2×3+1/2×3×4+、、、+1/20×21×22=?请光速回答!
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
解:1/1*2*3=(1/1*2-1/2*3)/2
1/2*3*4=(1/2*3-1/3*4)/2
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1/20*21*22=(1/20*21-21*22)/2
1/1*2*3+1/2*3*4+1/3*4*5+....+1/20*21*22
=(1/1*2-1/2*3)/2+(1/2*3-1/3*4)/2+ ----- +(1/20*21-1/21*22)/2
=(1/1*2-1/2*3+1/2*3-1/3*4+ ----- +1/20*21-1/21*22)/2
=(1/2-1/21*22)/2
=115/21*22
1/1*2*3+1/2*3*4+1/3*4*5+1/4*5*6+……+1/20*21*22=0.5(1/1*2-1/2*3+1/2*3-1/3*4....)=0.5*(0.5-1/21*22)
1/(1*2*3)+1/(2*3*4)+...+1/(20*21*22)
=1/2(1/1*2-1/2*3)+1/2(1/2*3-1/3*4)+...+1/2(1/20*21-1/21*22)
=1/2(1/1*2-1/2*3+1/2*3-1/3*4+...+1/20*21-1/21*22)
=1/2(1/1*2-1/21*22)
=1/2*115/231
=115/462