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计算:(1-1/2²)(1-1/3²)(1-1/4²)...(1-1/2007²)
过程详细准确!清晰!
(1-1/2²)(1-1/3²)(1-1/4²)...(1-1/2007²)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4)...(1+1/2007)(1-1/2007)
=(3/2)(1/2)(4/3)(2/3)(5/4)(3/4)...(2008/2007)(2006/2007)
=(1/2)(2008/2007)
=1004/2007
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