(1-1/2²)×(1-1/3²)……(1-1/2005²)×(1-1/2006²)平方是在分母的地方
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/26 02:35:26
![(1-1/2²)×(1-1/3²)……(1-1/2005²)×(1-1/2006²)平方是在分母的地方](/uploads/image/z/654301-37-1.jpg?t=%EF%BC%881-1%2F2%26%23178%3B%EF%BC%89%C3%97%EF%BC%881-1%2F3%26%23178%3B%EF%BC%89%E2%80%A6%E2%80%A6%EF%BC%881-1%2F2005%26%23178%3B%EF%BC%89%C3%97%EF%BC%881-1%2F2006%26%23178%3B%EF%BC%89%E5%B9%B3%E6%96%B9%E6%98%AF%E5%9C%A8%E5%88%86%E6%AF%8D%E7%9A%84%E5%9C%B0%E6%96%B9)
(1-1/2²)×(1-1/3²)……(1-1/2005²)×(1-1/2006²)平方是在分母的地方
(1-1/2²)×(1-1/3²)……(1-1/2005²)×(1-1/2006²)
平方是在分母的地方
(1-1/2²)×(1-1/3²)……(1-1/2005²)×(1-1/2006²)平方是在分母的地方
(1-1/2²)×(1-1/3²)……(1-1/2005²)×(1-1/2006²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/2005)(1+1/2005)(1-1/2006)(1+1/2006)
=(1/2)*(2007/2006)
=2007/4012
(1-1/2²)×(1-1/3²)……(1-1/2005²)×(1-1/2006²)
=(1+1/2)×(1-1/2)×(1+1/3)×(1-1/3)×……×(1+1/2005)×(1-1/2005)×(1+1/2006)×(1-1/2006)
=(1+1/2)×(1+1/3)×……×(1+1/2005)×(1+1/2006)×(1-1/2)...
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(1-1/2²)×(1-1/3²)……(1-1/2005²)×(1-1/2006²)
=(1+1/2)×(1-1/2)×(1+1/3)×(1-1/3)×……×(1+1/2005)×(1-1/2005)×(1+1/2006)×(1-1/2006)
=(1+1/2)×(1+1/3)×……×(1+1/2005)×(1+1/2006)×(1-1/2)×(1-1/3)×……×(1-1/2005)×(1-1/2006)
=3/2×4/3×……×2006/2005×2007/2006×1/2×2/3×……×2004/2005×2005/2006
=2007/2×1/2006
=2007/4012
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