Infinite product whose entries tend to 1 rapidly

Question

Does the following infinite product converge and what is the limit if it exists?

$$\prod_{i = 1}^{\infty} \frac{2^i}{2^i+1}$$

Answer 1

Hint: try writing it as $\prod_{i=1}^\infty \dfrac{1}{1 + 2^{-i}}$.