Finding the limit of a sequence? Is it possible to find the limit of the sequence defined by:
 $$a_n = \left(1+ \frac{1}{2}\right)\left(1+\frac{1}{4}\right)\cdots\left(1+\frac{1}{2^n}\right)$$
I have proved that it converges.

WolframAlpha comes up with this solution:
\begin{align}
\prod_{n=1}^\infty \left( 1 + \frac{1}{2^n} \right)
&= \frac{(-1;\frac{1}{2})_\infty}{2} \\
&= 2.3842310290313\ldots
\end{align}
where $(a;q)_n$ is the $q$-Pochhammer symbol (link):
$$
(a;q)_n
= \prod_{k=0}^{n-1} (1 - a q^k)
$$
