(1-1/2X1/2)X(1-3/1X3/1)X……X(1-1/2005X1/2005)

问题描述:

(1-1/2X1/2)X(1-3/1X3/1)X……X(1-1/2005X1/2005)

(1-1/2X1/2)X(1-3/1X3/1)X……X(1-1/2005X1/2005)
=(1+1/2)×(1-1/2)×(1+1/3)×(1-1/3)×(1+1/4)×(1-1/4)×...×(1+1/2005)×(1-1/2005)
=3/2×1/2×4/3×2/3×5/4×3/4×...×2006/2005×2004/2005
=1/2×2006/2005
=1003/2005