I need a help with this limit $\lim_{x\rightarrow \infty} \left(\frac{a^{1/x}+b^{1/x}}{2}\right)^x = \sqrt{ab}$
Proving that: $\lim\limits_{n\to\infty} \left(\frac{a^{\frac{1}{n}}+b^{\frac{1}{n}}}{2}\right)^n =\sqrt{ab}$