计算:(1-1/2²)(1-1/3²)......(1-1/2005²)(1-1/2006
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计算:(1-1/2²)(1-1/3²)......(1-1/2005²)(1-1/2006²)
![计算:(1-1/2²)(1-1/3²)......(1-1/2005²)(1-1/2006](/uploads/image/z/3802464-0-4.jpg?t=%E8%AE%A1%E7%AE%97%EF%BC%9A%EF%BC%881-1%2F2%26%23178%3B%EF%BC%89%EF%BC%881-1%2F3%26%23178%3B%EF%BC%89......%EF%BC%881-1%2F2005%26%23178%3B%EF%BC%89%EF%BC%881-1%2F2006)
(1-1/2²)(1-1/3²)(1-1/4²)…(1-1/2005²)(1-1/2006²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)(1-1/5)(1+1/5)(1-1/6)(1+1/6)(1-1/7)(1+1/7)(1-1/8)(1+1/8)……(1-1/2005)(1+1/2005)(1-1/2006)(1+1/2006)
=1/2×3/2×2/3×4/3×3/4.2004/2005×2006/2005×2005/2006×2007/2006
-----注意:除了第1分数和最后一个分数外,全约分了.
=1/2×2007/2006
=2007/4012
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)(1-1/5)(1+1/5)(1-1/6)(1+1/6)(1-1/7)(1+1/7)(1-1/8)(1+1/8)……(1-1/2005)(1+1/2005)(1-1/2006)(1+1/2006)
=1/2×3/2×2/3×4/3×3/4.2004/2005×2006/2005×2005/2006×2007/2006
-----注意:除了第1分数和最后一个分数外,全约分了.
=1/2×2007/2006
=2007/4012