计算:(1-2的负2次方)(1-3的负2次方)(1-4的负2次方)…(1-2010的负2次方)(1-2011的负2次方)
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(1-2的负2次方)(1-3的负2次方)(1-4的负2次方)…(1-2010的负2次方)(1-2011的负2次方)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4)……(1+1/2010)(1-1/2010)(1+1/2011)(1-1/2011)
=3/2×4/3×5/4×……×2011/2010×2012/2011×1/2×2/3×3/4×……×2009/2010×2010/2011
=2012/2×1/2011
=1006/2011
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4)……(1+1/2010)(1-1/2010)(1+1/2011)(1-1/2011)
=3/2×4/3×5/4×……×2011/2010×2012/2011×1/2×2/3×3/4×……×2009/2010×2010/2011
=2012/2×1/2011
=1006/2011
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