(1-1/2²)×(1-1/3²)×(1-1/4²)…(1-1/2007²)×(1-1/2008²)
问题描述:
(1-1/2²)×(1-1/3²)×(1-1/4²)…(1-1/2007²)×(1-1/2008²)
答
(1-1/2²)×(1-1/3²)×(1-1/4²)…(1-1/2007²)×(1-1/2008²)=((1-1/2)×(1-1/3)×(1-1/4)×…×(1-1/2007)×(1-1/2008))×((1+1/2)×(1+1/3)×(1+1/4)×…×(1+1/2007)×(1+1/2008))=(1/2×2...