Question

因式分解(1-1/2^)(1-1/3^)(1-1/4^)……(1-1/2007^)

Answer 1

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

=(1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4)……(1+1/2006)(1-1/2006)(1+1/2007)(1-1/2007)

=(3/2)*(1/2)*(4/3)*(2/3)*(5/4)*(3/4)*……*(2007/2006)*(2005/2006)*(2008/2007)*(2006/2007)

=(1/2)*(2008/2007)

=1004/2007