巧算:(1-2∧2/1)(1-3∧2/1)(1-4∧2/1).(1-2008∧2/1)∧右为次方／右为分子

Question

巧算:(1-2∧2/1)(1-3∧2/1)(1-4∧2/1).(1-2008∧2/1)
∧右为次方／右为分子

Answer 1

显然1- 1/2^2=(1-1/2)(1+1/2)=1/2 * 3/21- 1/3^2=(1-1/3)(1+1/3)=2/3 * 4/31- 1/4^2=(1-1/4)(1+1/4)=3/4 * 5/4……1- 1/2007^2=(1-1/2007)(1+1/2007)=2006/2007 * 2008/20071- 1/2008^2=(1-1/2008)(1+1/2008)=2007/2...