sequences and series - $underset{nrightarrow +infty }{overset{}{lim }} left(sqrt[n]{2} -1right)^{n} =0$

Prove that:

$$\underset{n\rightarrow +\infty }{\overset{}{\lim }} \ \left(\sqrt[n]{2} -1\right)^{n} =0$$

I would like a solution without integral, limit of real functions or others advanced methods.
I thought $\underset{n\rightarrow +\infty }{\overset{}{\lim }} \ 2\left(1- \frac{1}{\sqrt[n]2}\right)^{n} =0$ but I don't know how to continue.

Answer

It is a limit of the form
$$0^{\infty}$$

so it is not an indeterminate form, it converges to $0$.