(1-0.25)乘[1-(1/9)]乘[1-(1/16)乘[1-(1/25)].乘[1-(1/2005*2)]等于多少?
问题描述：
(1-0.25)乘[1-(1/9)]乘[1-(1/16)乘[1-(1/25)].乘[1-(1/2005*2)]等于多少?
答
(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