Find a formula for a sequence $\{\sqrt{3},\sqrt{3\sqrt{3}},\sqrt{3\sqrt{3\sqrt{3}}},...\}$ I'm trying to find a formula for the following sequence:
$\{\sqrt{3},\sqrt{3\sqrt{3}},\sqrt{3\sqrt{3\sqrt{3}}},...\}$
I thought of solving it recursively and I got this formula:
$a_{n}=\sqrt{3*a_{n-1}}$
$a_{0}=1$
Is there a better and non-recursive formula for the given sequence? 

If we start with $a_0$, what about $a_n=3^{\left(1-\frac{1}{2^{n+1}}\right)}$? Note that the terms are $3^{1/2}$, $3^{3/4}$, $3^{7/8}$, and so on.
