小学数奥题：(1+2/5) ×(1-2/5) ×(1+2/7) ×(1-2/7) ×…………×(1+2/2005) ×(1-2/2005)
问题描述：
小学数奥题：(1+2/5) ×(1-2/5) ×(1+2/7) ×(1-2/7) ×…………×(1+2/2005) ×(1-2/2005)
答
(1+2/5)×(1-2/5)×(1+2/7)×(1-2/7)×.......×(1+2/2005)×(1-2/2005)
=7/5×3/5×9/7×5/7×...×2007/2005×2003/2005
=(7/5×9/7×...×2007/2005)×(3/5×5/7×...×2003/2005)
=2007/5×3/2005
=6021/10025
答
(2007/5) ×(3/2005) (7/5)x(3/5)x(9/7)x(5/7)x...x(2007/5)x(2003/2005)=[(7/5)x(9/7)x.X(2007/5)]x[(3/5)x(5/7)x...x(2003/2005)]=(2007/5)x(3/2005)=6021/10025