I have been trying to evaluate the following limit
$$ \lim_{m \rightarrow \infty} \prod_{k = 0}^{m} \frac{n^{2^{k}} - 1}{n^{2^{k}}} $$
for fixed natural number $n > 1.$
Plugging some finite products into WolframAlpha it seems that the product decays very slowly to zero, but I'm unsure whether this limit actually converges to zero or to some other number. Any tips would be appreciated.