The math teacher of a friend of mine gave him this question on a test. He then asked me if I could solve it, but I had no idea how to begin. It goes like this.
Find the value of the following infinite product: $$\prod\limits_{n=1}^{\infty} \biggl(1-\frac{1}{2^{n}}\biggr)$$
It does indeed converge, but how does does one calculate the value? I did plug it into WolframAlpha, and the answer is about 0.288.