While working on a different problem, I've run into the infinite product: $$\prod_{i=1}^\infty (1-2^{-i}) $$ Which I'm reasonably sure should be equal to $1-\frac{1}{\sqrt{2}}$. EDIT: It definitely doesn't equal this value, nevermind
However, I don't really have any notion of how to work with / prove things about an infinite product of this form. I tried considering the log of the partial products, but that doesn't seem to make the numerical value any easier to evaluate.
Doing some googling, these sorts of products seem to be called Euler products, or q series (see here: http://mathworld.wolfram.com/q-PochhammerSymbol.html). However, I can't find much or anything online about methods for finding their value. Is there any process that would yield a precise answer in this case?
