一道数学题:巧算(思路和过程)
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:2024/07/03 13:27:47
一道数学题:巧算(思路和过程)
2*(1*1/3+1/3*1/5+1/5*1/7+1/7*1/9+…1/99*1/101)
2*(1*1/3+1/3*1/5+1/5*1/7+1/7*1/9+…1/99*1/101)
![一道数学题:巧算(思路和过程)](/uploads/image/z/368105-41-5.jpg?t=%E4%B8%80%E9%81%93%E6%95%B0%E5%AD%A6%E9%A2%98%EF%BC%9A%E5%B7%A7%E7%AE%97%EF%BC%88%E6%80%9D%E8%B7%AF%E5%92%8C%E8%BF%87%E7%A8%8B%EF%BC%89)
2*(1*1/3+1/3*1/5+1/5*1/7+1/7*1/9+…1/99*1/101)
=2*[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*(1/99-1/100)]
=(1-1/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+.+(1/99-1/100)
=1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+.+1/99-1/100
=1-1/100
=99/100
=2*[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*(1/99-1/100)]
=(1-1/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+.+(1/99-1/100)
=1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+.+1/99-1/100
=1-1/100
=99/100