Computation of $\sum_{i=0}^{m-1} n^{1/2^i}$

Question

Basically, I'm just having issues computing this sum:

$$ \sum_{i=0}^{m-1} n^{1/2^i} $$

where $m = \log_{2}({\log_{2}({n})})$.

I need it in terms of $n$, as it's part of a runtime that I'm attempting to bound in order to get its $\Theta$.