
计算(1-2*2分之1)(1-3*2分之1)....(1-2008*2分之1)(1-2009*2分之1)
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(1-2^2分之1)(1-3^2分之1)....(1-2008^2分之1)(1-2009^2分之1)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)……(1+1/2008)(1-1/2008)(1+1/2009)(1-1/2009)
=3/2×4/3×……×2009/2008×2010/2009×1/2×2/3×……×2007/2008×2008/2009
=2010/2×1/2009
=1005/2009
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)……(1+1/2008)(1-1/2008)(1+1/2009)(1-1/2009)
=3/2×4/3×……×2009/2008×2010/2009×1/2×2/3×……×2007/2008×2008/2009
=2010/2×1/2009
=1005/2009
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2012-06-30
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(1-2^2分之1)(1-3^2分之1)....(1-2008^2分之1)(1-2009^2分之1)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)……(1+1/2008)(1-1/2008)(1+1/2009)(1-1/2009)
=3/2×4/3×……×2009/2008×2010/2009×1/2×2/3×……×2007/2008×2008/2009
=2010/2×1/2009
=1005/2009
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)……(1+1/2008)(1-1/2008)(1+1/2009)(1-1/2009)
=3/2×4/3×……×2009/2008×2010/2009×1/2×2/3×……×2007/2008×2008/2009
=2010/2×1/2009
=1005/2009
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2012-07-05
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(1-2^2分之1)(1-3^2分之1)....(1-2008^2分之1)(1-2009^2分之1)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)……(1+1/2008)(1-1/2008)(1+1/2009)(1-1/2009)
=3/2×4/3×……×2009/2008×2010/2009×1/2×2/3×……×2007/2008×2008/2009
=2010/2×1/2009
=1005/2009
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)……(1+1/2008)(1-1/2008)(1+1/2009)(1-1/2009)
=3/2×4/3×……×2009/2008×2010/2009×1/2×2/3×……×2007/2008×2008/2009
=2010/2×1/2009
=1005/2009
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