计算:(1-1/2²)x(1-1/3²)X(1-1/4²)×…x(1-1/2015²）x(1-1/2016²)
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解决时间 2021-11-14 10:07
- 提问者网友：書生途
- 2021-11-14 04:54
计算:(1-1/2²)x(1-1/3²)X(1-1/4²)×…x(1-1/2015²）x(1-1/2016²)
最佳答案
- 五星知识达人网友：千夜
- 2021-11-14 05:37
解：
(1- 1/2²)(1- 1/3²)...(1- 1/2016²)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)...(1+1/2016)(1-1/2016)
=(3/2)(1/2)(4/3)(2/3)...(2017/2016)(2015/2016)
=[(3/2)(4/3)...(2017/2016)][(1/2)(2/3)...(2015/2016)]
=(2017/2)(1/2016)
=2017/4032
(1- 1/2²)(1- 1/3²)...(1- 1/2016²)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)...(1+1/2016)(1-1/2016)
=(3/2)(1/2)(4/3)(2/3)...(2017/2016)(2015/2016)
=[(3/2)(4/3)...(2017/2016)][(1/2)(2/3)...(2015/2016)]
=(2017/2)(1/2016)
=2017/4032
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