9000064009

Find the limit of the following sequence. $${\left({(\frac{\sqrt[n]{2}}{n}+\sqrt[n]{2})}^n\right)}_{n=1}^{\mathrm{\infty }}$$ Hint: The limit of the sequence ${({(1+\frac{1}{n})}^n)}_{n=1}^{\mathrm{\infty }}$ is the Euler number $\mathrm{e}$.