计算:(1-1/2²)(1-1/3²)......(1-1/2004²)(1-1/2005²)

问题描述:

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...