## Interesting pi notation problem

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

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