逆用平方差公式
(1-1/2²)*(1-1/3²)*(1-1/4²)*。。。*(1-1/2008²)
=[(1+1/2)(1-1/2)]*[(1+1/3)(1-1/3)]*[(1+1/4)(1-1/4)]*。 。。([(1+1/2008)(1-1/2008)]
=(3/2)(1/2)(4/3)(2/3)(5/4)(3/4)。。。(2009/2008)(2007/2008)
=[(1/2)(2/3)(3/4))(4/5)(5/6)(6/7)。 。。2006/2007)(2007/2008)][(3/2)(4/3)(5/4)。。。(2009/2008)]
=(1/2...全部
(1-1/2²)*(1-1/3²)*(1-1/4²)*。。。*(1-1/2008²)
=[(1+1/2)(1-1/2)]*[(1+1/3)(1-1/3)]*[(1+1/4)(1-1/4)]*。
。。([(1+1/2008)(1-1/2008)]
=(3/2)(1/2)(4/3)(2/3)(5/4)(3/4)。。。(2009/2008)(2007/2008)
=[(1/2)(2/3)(3/4))(4/5)(5/6)(6/7)。
。。2006/2007)(2007/2008)][(3/2)(4/3)(5/4)。。。(2009/2008)]
=(1/2008)*(2009/2)
=2009/4016
。收起