What is the Limit of $(1+\frac{1}{2})(1+\frac{1}{4})...(1+\frac{1}{2^n})$ at n = $\infty$?
At first I think it is divergent but it is surely convergent to something between $2$ and $3$. More exactly it is between $2.3$ to $2.4$. something about $2.38$. but I don't know how to find its limit. What can we say about rationality of the answer? (Is it rational or irrational?)
My question is made of two parts. first finding the limit and second, discussing about its rationality.