Question

计算:(1-1/2^2)(1-1/3^2)(1-1/4^2)……(1-1/2013^2).

Answer 1

(1-1/2^2)(1-1/3^2)(1-1/4^2)……(1-1/2013^2).

=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)……(1-1/2013)(1+1/2013)

=1/2 × 3/2×2/3 × 4/3×3/4 × 5/4×4/5 × ……×2012/2013 ×2014/2013

=1/2×2014/2013

=1007/2013