1/1*3+1/3*5+1/5*7+1/7*9.1/17*19+1/19*21怎么做?
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/21 15:14:33
1/1*3+1/3*5+1/5*7+1/7*9.1/17*19+1/19*21怎么做?
要简便运算
要简便运算
![1/1*3+1/3*5+1/5*7+1/7*9.1/17*19+1/19*21怎么做?](/uploads/image/z/3228216-24-6.jpg?t=1%2F1%2A3%2B1%2F3%2A5%2B1%2F5%2A7%2B1%2F7%2A9.1%2F17%2A19%2B1%2F19%2A21%E6%80%8E%E4%B9%88%E5%81%9A%3F)
1/1*3+1/3*5+1/5*7+1/7*9.1/17*19+1/19*21
=1/2*(1-1/3)+1/2*(1/3-1/5)+1/2*(1/5-1/7)+1/2*(1/7-1/9)+.+1/2*(1/17-1/19)+1/2*(1/19-1/21)
=1/2*(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+.+1/17-1/19+1/19-1/21)
=1/2*(1-1/21)
=1/2*20/21
=10/21
=1/2*(1-1/3)+1/2*(1/3-1/5)+1/2*(1/5-1/7)+1/2*(1/7-1/9)+.+1/2*(1/17-1/19)+1/2*(1/19-1/21)
=1/2*(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+.+1/17-1/19+1/19-1/21)
=1/2*(1-1/21)
=1/2*20/21
=10/21