(1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)*(1+1/4)*(1-1/4)*.*(1+1/99)*(1-1/99)= ("*"=乘号)用合适的方法算出来,
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/23 16:42:38
![(1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)*(1+1/4)*(1-1/4)*.*(1+1/99)*(1-1/99)= (](/uploads/image/z/7556815-55-5.jpg?t=%281%2B1%2F2%29%2A%281-1%2F2%29%2A%281%2B1%2F3%29%2A%281-1%2F3%29%2A%281%2B1%2F4%29%2A%281-1%2F4%29%2A.%2A%281%2B1%2F99%29%2A%281-1%2F99%29%3D+%28%22%2A%22%3D%E4%B9%98%E5%8F%B7%EF%BC%89%E7%94%A8%E5%90%88%E9%80%82%E7%9A%84%E6%96%B9%E6%B3%95%E7%AE%97%E5%87%BA%E6%9D%A5%2C)
(1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)*(1+1/4)*(1-1/4)*.*(1+1/99)*(1-1/99)= ("*"=乘号)用合适的方法算出来,
(1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)*(1+1/4)*(1-1/4)*.*(1+1/99)*(1-1/99)= ("*"=乘号)
用合适的方法算出来,
(1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)*(1+1/4)*(1-1/4)*.*(1+1/99)*(1-1/99)= ("*"=乘号)用合适的方法算出来,
(1-1/2)*(1+1/2)*(1-1/3)*(1+1/3)...*(1-1/99)*(1+1/99)
先算各个括号里的
=(1/2)*(3/2)*(2/3)*(4/3)*(3/4)*(5/4)*...(98/99)*(100/99)
=分子与分母相同的就相抵消
最后剩下
=(1/2)*(100/99)
=50/99
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