计算(1-(2²分之1))(1-(3²分之1))(1-(4²分之1))···(1-(2013²分之1))
答案:2 悬赏:30
解决时间 2021-03-13 08:19
- 提问者网友:写不出迷人情诗
- 2021-03-12 13:09
计算(1-(2²分之1))(1-(3²分之1))(1-(4²分之1))···(1-(2013²分之1))
最佳答案
- 二级知识专家网友:迷人小乖乖
- 2021-03-12 13:39
(1-1/2²)(1-1/3²)(1-1/4²)...(1-1/2013²)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4)...(1+1/2013)(1-1/2013)
=(3/2)(1/2)(4/3)(2/3)(5/4)(3/4)...(2014/2013)(2012/2013)
=[(3/2)(4/3)(5/4)...(2014/2013)][(1/2)(2/3)(3/4)...(2012/2013)]
=[(3×4×5×...×2014)/(2×3×4×...×2013)][(1×2×3×...×2012)/(2×3×4×...×2013)]
=(2013/2)(1/2012)
=2013/4024
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4)...(1+1/2013)(1-1/2013)
=(3/2)(1/2)(4/3)(2/3)(5/4)(3/4)...(2014/2013)(2012/2013)
=[(3/2)(4/3)(5/4)...(2014/2013)][(1/2)(2/3)(3/4)...(2012/2013)]
=[(3×4×5×...×2014)/(2×3×4×...×2013)][(1×2×3×...×2012)/(2×3×4×...×2013)]
=(2013/2)(1/2012)
=2013/4024
全部回答
- 1楼网友:而你却相形见绌
- 2021-03-12 14:46
没看懂什么意思?
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