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? 

Let $b_n = \ln( a_n )$, then according to $a_n = \sqrt{3a_{n-1}}$, we have:
$b_n = \frac{1}{2}[ \ln(3)+b_{n-1} ]$ with $b_0=0$
which is a classical problem. We can easily find its solution:
$b_n = \ln(3)[ 1 - (\frac{1}{2})^n]$.
It is trivial to convert $b_n$ to $a_n = 3^{1-(\frac{1}{2})^n}$ 
