How to prove $\limsup_{n\to \infty} \sqrt[n]{|a_n|}=\limsup_{n\to \infty} \sqrt[n]{|a_{n+1}-a_n|}$ if $\{a_n\}$ diverges
Is it true that $\limsup\sqrt[n]{|a_n|}=\limsup\sqrt[n]{|a_n-a_{n-1}|}$, ($n>1$), where $\{a_n\}$ does not have a finite limit?