I'm going over a proof, whose last step is the following statement:

If $ k = (1-\epsilon )\cdot \log\_{2}(n)$

$$ \lim\_{n\rightarrow \infty} 1-k(1-2^{-k})^{(n/k)} = 1$$

I'm trying to understand why this k ensures that the limit converges to 1.