(1-1/2²)(1-1/3²)(1-1/4²)(1-1/5²)……(1-1/2006²)(1-1/2007²)
问题描述：
(1-1/2²)(1-1/3²)(1-1/4²)(1-1/5²)……(1-1/2006²)(1-1/2007²)
答
用平方差
原式=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/2007)(1+1/2007)
=(1/2)(3/2)(2/3)(4/3)……(2006/2007)(2008/2007)
中间约分
=(1/2)(2008/2007)
=1004/2007