计算：（1--1/2^2）*（1--1/3^2）*（1--1/4^2）*....*(1--1/2010^2)*(1--1/2011^2)
2个回答
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(1-1/2²)(1-1/3²)...(1-1/2010²)(1-1/2011²)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)...(1+1/2010)(1-1/2010)(1+1/2011)(1-1/2011)
=(3/2)(1/2)(4/3)(2/3)...(2011/2010)(2009/2010)(2012/2011)(2010/2011)
=[(3/2)(4/3)...(2012/2011][(1/2)(2/3)...(2010/2011)]
=[(3×4×...×2012)/(2×3×...×2011)][(1×2×...×2010)/(2×3×...×2011)]
=(2012/2)(1/2011)
=1006/2011
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)...(1+1/2010)(1-1/2010)(1+1/2011)(1-1/2011)
=(3/2)(1/2)(4/3)(2/3)...(2011/2010)(2009/2010)(2012/2011)(2010/2011)
=[(3/2)(4/3)...(2012/2011][(1/2)(2/3)...(2010/2011)]
=[(3×4×...×2012)/(2×3×...×2011)][(1×2×...×2010)/(2×3×...×2011)]
=(2012/2)(1/2011)
=1006/2011
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(1-1/2²)(1-1/3²)...(1-1/2010²)(1-1/2011²)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)...(1+1/2010)(1-1/2010)(1+1/2011)(1-1/2011)
=(3/2)(1/2)(4/3)(2/3)...(2011/2010)(2009/2010)(2012/2011)(2010/2011)
=[(3/2)(4/3)...(2012/2011][(1/2)(2/3)...(2010/2011)]
=[(3×4×...×2012)/(2×3×...×2011)][(1×2×...×2010)/(2×3×...×2011)]
=(2012/2)(1/2011)
=1006/2011
是不是？
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)...(1+1/2010)(1-1/2010)(1+1/2011)(1-1/2011)
=(3/2)(1/2)(4/3)(2/3)...(2011/2010)(2009/2010)(2012/2011)(2010/2011)
=[(3/2)(4/3)...(2012/2011][(1/2)(2/3)...(2010/2011)]
=[(3×4×...×2012)/(2×3×...×2011)][(1×2×...×2010)/(2×3×...×2011)]
=(2012/2)(1/2011)
=1006/2011
是不是？
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