(1-1/2²)×(1-1/3²)×…×(1-1/2009²)×(1-1/2010²)

问题描述:

(1-1/2²)×(1-1/3²)×…×(1-1/2009²)×(1-1/2010²)
1-1/2²=1/2×3/2,1-1/3²=2/3×4/3,以此类推……

(1-1/2²)×(1-1/3²)×…×(1-1/2009²)×(1-1/2010²)
=1/2×3/2×2/3×4/3×…×2008/2009×2010/2009×2009/2010×2011/2010
=1/2×2011/2010
=2011/4020