How to find $\lim_{n \to \infty } \frac{ \sum_{k=1}^{n}(1-(1-2^{-k})^n) }{\ln n}$

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How to find $$\lim_{n \to \infty } \frac{ \sum_{k=1}^{n}(1-(1-2^{-k})^n) }{\ln n}.$$ Is there a simple way?