1*2*3*4分之1+2*3*4*5分之1+…+17*18*19*20分之1(计算题)1/1*2*3*4+1/2*3*4*5…………+1/17*18*19*20=1/2(1/1*4-1/2*3+1/2*5-1/3*4+1/3*6-1/4*5……1/17*20-1/18*19)=1/2(1/1*4+1/2*5+1/3*6……1/17*20-(1/2*3+1/3*4……1/18*19))=1/2*(1/3*(1-
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/06 16:56:41
![1*2*3*4分之1+2*3*4*5分之1+…+17*18*19*20分之1(计算题)1/1*2*3*4+1/2*3*4*5…………+1/17*18*19*20=1/2(1/1*4-1/2*3+1/2*5-1/3*4+1/3*6-1/4*5……1/17*20-1/18*19)=1/2(1/1*4+1/2*5+1/3*6……1/17*20-(1/2*3+1/3*4……1/18*19))=1/2*(1/3*(1-](/uploads/image/z/23375-47-5.jpg?t=1%2A2%2A3%2A4%E5%88%86%E4%B9%8B1%2B2%2A3%2A4%2A5%E5%88%86%E4%B9%8B1%2B%E2%80%A6%2B17%2A18%2A19%2A20%E5%88%86%E4%B9%8B1%EF%BC%88%E8%AE%A1%E7%AE%97%E9%A2%98%EF%BC%891%2F1%2A2%2A3%2A4%2B1%2F2%2A3%2A4%2A5%E2%80%A6%E2%80%A6%E2%80%A6%E2%80%A6%2B1%2F17%2A18%2A19%2A20%3D1%2F2%281%2F1%2A4-1%2F2%2A3%2B1%2F2%2A5-1%2F3%2A4%2B1%2F3%2A6-1%2F4%2A5%E2%80%A6%E2%80%A61%2F17%2A20-1%2F18%2A19%29%3D1%2F2%281%2F1%2A4%2B1%2F2%2A5%2B1%2F3%2A6%E2%80%A6%E2%80%A61%2F17%2A20-%281%2F2%2A3%2B1%2F3%2A4%E2%80%A6%E2%80%A61%2F18%2A19%29%29%3D1%2F2%2A%281%2F3%2A%281-)
1*2*3*4分之1+2*3*4*5分之1+…+17*18*19*20分之1(计算题)1/1*2*3*4+1/2*3*4*5…………+1/17*18*19*20=1/2(1/1*4-1/2*3+1/2*5-1/3*4+1/3*6-1/4*5……1/17*20-1/18*19)=1/2(1/1*4+1/2*5+1/3*6……1/17*20-(1/2*3+1/3*4……1/18*19))=1/2*(1/3*(1-
1*2*3*4分之1+2*3*4*5分之1+…+17*18*19*20分之1(计算题)
1/1*2*3*4+1/2*3*4*5…………+1/17*18*19*20
=1/2(1/1*4-1/2*3+1/2*5-1/3*4+1/3*6-1/4*5……1/17*20-1/18*19)
=1/2(1/1*4+1/2*5+1/3*6……1/17*20-(1/2*3+1/3*4……1/18*19))
=1/2*(1/3*(1-1/4+1/2-1/5+1/3-1/6+1/4-1/7……1/17-1/20)-(1/2-1/3+1/3-1/4……1/18-1/19))
=1/2*(1/3*(1+1/2+1/3-1/18-1/19-1/20)-(1/2-1/19))
=1/2*(1/3*(5/18-1/19-1/20+3/19))
=1/6*(5/18+2/19-1/20)
=1139/(6*19*180)
=1139/20520
1*2*3*4分之1+2*3*4*5分之1+…+17*18*19*20分之1(计算题)1/1*2*3*4+1/2*3*4*5…………+1/17*18*19*20=1/2(1/1*4-1/2*3+1/2*5-1/3*4+1/3*6-1/4*5……1/17*20-1/18*19)=1/2(1/1*4+1/2*5+1/3*6……1/17*20-(1/2*3+1/3*4……1/18*19))=1/2*(1/3*(1-
1*2*3*4分之1+2*3*4*5分之1+…+17*18*19*20
=(1/6)(1+1/2+1/3-1/18-1/19-1/20)-(1/2)(1/2-1/19)
=(1/6)(11/6-1/18-1/19-1/20)-17/76
=5729/20520-17/76
=1139/20520