Is it trivial that $\limsup\limits_{n\to\infty}\sqrt[n]{|a_{n+1}|}=\limsup\limits_{n\to\infty}\sqrt[n]{|a_{n}|}$

Question

Is it correct that $\underset{n\to\infty}{\limsup_{n\to\infty}\sqrt[n]{|a_{n+1}|}=\limsup}\sqrt[n]{|a_{n}|}$? i know its correct for regular $ \lim $ but im not sure for $ \limsup $. Also, is it correct that $ \limsup_{n\to\infty}\sqrt[n+1]{|a_{n+1}|}=\limsup_{n\to\infty}\sqrt[n]{|a_{n+1}|}=\underset{n\to\infty}{\limsup}\sqrt[n]{|a_{n}|} $ ?

And how can I prove those claims? Thanks.