1/1*3+1/3*5+1/5*7+.1/17*19+1/19*21怎么简便计算?

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/25 09:40:32
1/1*3+1/3*5+1/5*7+.1/17*19+1/19*21怎么简便计算?1/1*3+1/3*5+1/5*7+.1/17*19+1/19*21怎么简便计算?1/1*3+1/3*5+1/5*7+

1/1*3+1/3*5+1/5*7+.1/17*19+1/19*21怎么简便计算?
1/1*3+1/3*5+1/5*7+.1/17*19+1/19*21怎么简便计算?

1/1*3+1/3*5+1/5*7+.1/17*19+1/19*21怎么简便计算?
1/1*3+1/3*5+1/5*7+.1/17*19+1/19*21
=【(1-1-3)+(1/3-1/5)+(1/5-1/7)……+(1/17-1/19)+(1/19-1/21)】÷2
=【1-1-3+1/3-1/5+1/5-1/7……+1/17-1/19+1/19-1/21】÷2
=【1-1/21】÷2
=20/21÷2
=10/21
很高兴为你解答,

分数裂项
1/(1×3)=(1-1/3)÷2
1/(3×5)=(1/3-1/5)÷2
......
1/(19×21)=(1/19-1/21)÷2
原式=(1-1/3+1/3-1/5+...+1/19-1/21)÷2
=(1-1/21)÷2
=20/21÷2
=10/21

1/1*3+1/3*5+1/5*7+....1/17*19+1/19*21
=1/2(1/1-1/3+1/3-1/5+……+1/17-1/19+1/19-1/21)
=1/2(1-1/21)
=1/2*20/21
=10/21

1/1*3+1/3*5+1/5*7+....1/17*19+1/19*21
=(1/2)*(1-1/3+1/3-1/5+1/5-1/7+....+1/17-1/19+1/19-1/21)
=(1/2)*(1-1/21)
=(1/2)*(20/21)
=10/21
不懂可追问
满意请采纳
谢谢