what is the closed form if any of the following
$$ \left(1+\frac{1}{1!}\right)\left(1+\frac{1}{2!}\right)\left(1+\frac{1}{3!}\right)...$$
I thought of this while solving a problem like this-
$$\left(1+\frac{1}{3^{2^0}}\right)\left(1+\frac{1}{3^{2^1}}\right)\left(1+\frac{1}{3^{2^2}}\right)\cdots$$ the answer is $\frac{3}{2}$ using the fact that because every integer can be written in base $2$ this infinite product gives every possible power of $3$.