作业帮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：2024/05/08 17:23:05
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
-----
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