Question

(1-1/2^2)(1-1/3^2)(1-1/4^2).(1-1/2006^2)(1-1/2007^2)=

Answer 1

用平方差公式得

原式=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/2006)(1+1/2006)(1-1/2007)(1+1/2007)

=(1/2)(3/2)(2/3)(4/3)……(2005/2006)/(2007/2006)(2006/2007)(2008/2007)

中间约分

=(1/2)(2008/2007)

=1004/2007