(1-1/2的平方)(1-1/3的平方)(1-1/4的平方).(1-1/1999的平方)(1-1/2000的平方)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4).(1-1/1999)(1+1/1999)(1-1/2000)(1+1/2000)
=1/2×3/2×2/3×4/3×.3/4×5/4.1998/1999×2000/1999×1999/2000×2001/2000
=1/2×2001/2000
=2001/4000
(1-1/2的平方)(1-1/3的平方)(1-1/4的平方).(1-1/1999的平方)(1-1/2000的平方)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4).(1-1/1999)(1+1/1999)(1-1/2000)(1+1/2000)
=1/2×3/2×2/3×4/3×.3/4×5/4.1998/1999×2000/1999×1999/2000×2001/2000
=1/2×2001/2000
=2001/4000