Today my lecturer put up on the board that:
If $\lim\limits_{n\to\infty}\frac{a_{n+1}}{a_n}$ exists and $a_n>0$ then
$\displaystyle \limsup\limits_{n\to\infty}\left(a_n^{\frac{1}{n}}\right)=\lim_{n\to\infty}\frac{a_{n+1}}{a_n}$
however I am not sure why this is true, can somebody give me a hint or something as to how to go about proving this.
thanks for any help