Calculating Probability with Infinite Product: 0.28

[learnfrench]

I am actually trying to calculate a probability and hitting upon the infinite product:

$$\prod_{j=1}^{\infty}\frac{2^{j}-1}{2^{j}}$$

Any idea what this might be (it's about 0.28, but I want the formula).

 

[CRGreathouse]

I am actually trying to calculate a probability

that a binary matrix is nonsingular?

http://www.research.att.com/~njas/sequences/A048651 is the constant. There are several formulas there, but probably none that are 'the formula' you hoped to find.

 

[learnfrench]

This infinite product is basically a mathematical constant called Q in digital tree searching. There is some helpful information on http://mathworld.wolfram.com/InfiniteProduct.html and http://mathworld.wolfram.com/TreeSearching.html.