Interesting pi notation problem

Bipolarity

I've been trying to prove this using rigorous methods, without much success. I've been able to express as a binomial but that hasn't helped much.

Prove [tex]{\it evalb} \left( {\it and} \left( {\frac {1}{64}}<\prod _{i=1}^{1005}1/2\,{\frac {2\,i-1}{i}},\prod _{i=1}^{1005}1/2\,{\frac {2\,i-1}{i}}<1/44 \right) \right) [/tex]

1/64 < product((2*i-1)/(2*i), i = 1 .. 1005) and product((2*i-1)/(2*i), i = 1 .. 1005) < 1/44