Calculate the limit $$ \lim\limits_{ n \to \infty }\prod\limits_{k=0}^{n}{\left( 1-\frac{1}{2^{2^{k}}} \right)}. $$
It's bounded and monotonically, so I know it has the limit. But I can't get it. I used the wolfram and I got 0.350184……
The question for me is whether it have the specific num or something I neglect.
Any help would be appreciated!