计算:(1-1/2²)(1-1/3²)......(1-1/2004²)(1-1/2005²)
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计算:(1-1/2²)(1-1/3²)......(1-1/2004²)(1-1/2005²)
计算:(1-1/2²)(1-1/3²)......(1-1/2004²)(1-1/2005²)
计算:(1-1/2²)(1-1/3²)......(1-1/2004²)(1-1/2005²)
(1-1/2²)(1-1/3²)......(1-1/2004²)(1-1/2005²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3).(1-1/2005)(1+1/2005)
=1/2×3/2×2/3×4/3×...×2004/2005×2006/2005
=1/2×2/3×3/4×...×2004/2005×3/2×4/3×...×2006/2005
=1/2005×2006/2
=1003/2005;
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