根据a²-b²=(a-b)(a+b)得
1-1/2²=(1-1/2)(1+1/2)=(1/2)×(3/2)
1-1/3²=(1-1/3)(1+1/3)=(2/3)×(4/3)
1-1/4²=(1-1/4)(1+1/4)=(3/4)×(5/4)
……
1-1/2007²=(1-1/2007)(1+1/2007)=(2006/2007)×(2008/2007)
所有等式相乘
左侧=(1-1/2²)×(1-1/3²)×(1-1/4²)……×(1-1/2007²)
右侧=(1/2)×(3/2)×(2/3)×(4/3)×(3/4)×(5/4)×……×(2006/2007)×(2008/2007)=1/2×2008/2007=1004/2007
(1-1/2²)×(1-1/3²)×(1-1/4²)……×(1-1/2007²)=1004/2007