Calculate limit of $\sqrt[n]{2^n - n}$ Calculate limit of $\sqrt[n]{2^n - n}$.
I know that lim $\sqrt[n]{2^n - n} \le 2$, but don't know where to go from here.

Hint:
$\sqrt[n]{2^n - n} = 2 (1 - \frac{n}{2^n})^{\frac{1}{n}} = 2 ((1 - \frac{n}{2^n})^{\frac{2^n}{n}} )^{\frac{1}{2^n}}$
Now... Do you know Euler?
