作业帮1\1×3 + 1\2×4+ 1\3×5 …… +1\18×20
来源：学生作业帮 编辑：拍题作业网作业帮 分类：数学作业 时间：2024/05/17 14:56:31
1\1×3 + 1\2×4+ 1\3×5 …… +1\18×20
1\1×3 + 1\2×4+ 1\3×5 …… +1\18×20
1\1×3 + 1\2×4+ 1\3×5 …… +1\18×20
因为1/[n(n+2)]=1/2 × [(n+2)-n]/[n(n+2)]=1/2 × [1/n-1/(n+2)]
所以1\1×3 + 1\2×4+ 1\3×5 …… +1\18×20
=1/2×(1/1-1/3)+1/2×(1/2-1/4)+1/2×(1/3-1/5)+……+1/2×(1/18-1/20)
=1/2×(1/1-1/3+1/2-1/4+1/3-1/5+……+1/18-1/20)
=1/2×(1+1/2-1/19-1/20)
=1/2×531/380
=531/760
祝学习快乐
所以1\1×3 + 1\2×4+ 1\3×5 …… +1\18×20
=1/2×(1/1-1/3)+1/2×(1/2-1/4)+1/2×(1/3-1/5)+……+1/2×(1/18-1/20)
=1/2×(1/1-1/3+1/2-1/4+1/3-1/5+……+1/18-1/20)
=1/2×(1+1/2-1/19-1/20)
=1/2×531/380
=531/760
祝学习快乐
计算1/1×3+1/2×4+1/3×5……1/18×20
1\1×3 + 1\2×4+ 1\3×5 …… +1\18×20
1+2+3+4+5+…+18+19+20=
1/2*3*4+1/2*3*4+3*4*5+……1/18*19*20=
1/1*2*3+1/2*3*4+……+1/18*19*20
计算(1/2+1/3)+(2/3+1/4)+(3/4+1/5)……+(18/19+1/20)+(19/20+1/2)!
1/1×2×3×4+1/2×3×4×5+1/3×4×5×6+……+1/17×18×19×20
1/（1*3）+1/（2*4）+1/（3*5）+1/（4*6）……+1/（18*20）
| 1/3 - 1/2 | + | 1/4 - 1/3 | + | 1/5 - 1/4 | …… + | 1/2009
1×2×3×4分之3+2×3×4×5分之3+……+17×18×19×20分之3
23+22+21+20……+1+1+2+3+4+5……+55
1/2+1/3+2/3+1/4+2/4+3/4+1/5+2/5+3/5+4/5+1/6+……+17/20+18/20+1