(1-1/2)(1/3-1)(1-1/4)(1/5-1).(1-1/2004)(1/2005-1)

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(1-1/2)(1/3-1)(1-1/4)(1/5-1).(1-1/2004)(1/2005-1)
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(1-1/2)(1/3-1)(1-1/4)(1/5-1).(1-1/2004)(1/2005-1)
(1-1/2)(1/3-1)(1-1/4)(1/5-1).(1-1/2004)(1/2005-1)

(1-1/2)(1/3-1)(1-1/4)(1/5-1).(1-1/2004)(1/2005-1)
先确定符号为正 有1002个负数

∴原式=(1-1/2)(1-1/3)(1-1/4)(1-1/5)……(1-1/2004)(1-1/2005)
=1/2×2/3×3/4×……×2003/2004×2004/2005
=1/2005

(1-1/2)(1/3-1)(1-1/4)(1/5-1).....(1-1/2004)(1/2005-1)
=(1/2)(-2/3)(3/4)(-4/5)......(2003/2004)(-2004/2005)
=1/2005