大师作文网(1-0.25)乘[1-(1/9)]乘[1-(1/16)乘[1-(1/25)].乘[1-(1/2005*2)]等于多少?
来源：学生作业帮 编辑：大师作文网作业帮 分类：数学作业 时间：2024/11/19 18:13:28
(1-0.25)乘[1-(1/9)]乘[1-(1/16)乘[1-(1/25)].乘[1-(1/2005*2)]等于多少?
![(1-0.25)乘[1-(1/9)]乘[1-(1/16)乘[1-(1/25)].乘[1-(1/2005*2)]等于多少?](/uploads/image/z/7399485-45-5.jpg?t=%281-0.25%29%E4%B9%98%5B1-%281%2F9%29%5D%E4%B9%98%5B1-%281%2F16%29%E4%B9%98%5B1-%281%2F25%29%5D.%E4%B9%98%5B1-%281%2F2005%2A2%29%5D%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%3F)
(1-0.25)乘[1-(1/9)]乘[1-(1/16)乘[1-(1/25)].乘[1-(1/2005²)]
=(1-1/4)*(1-1/9)(1-1/16)(1-1/25)*.(1-1/2005²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)*.*(1-1/2005)(1+1/2005)
=1/2*3/2*2/3*4/3*3/4*4/5*5/4*.*2005/2004*2004/2005*2006/2005
=1/2*2006/2005
=1003/2005
=(1-1/4)*(1-1/9)(1-1/16)(1-1/25)*.(1-1/2005²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)*.*(1-1/2005)(1+1/2005)
=1/2*3/2*2/3*4/3*3/4*4/5*5/4*.*2005/2004*2004/2005*2006/2005
=1/2*2006/2005
=1003/2005
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