Does limsup √(a_{n+1}/a_n) = √(limsup(a_{n+1}/a_n))?

[diligence]

Hi,

Is it true that $limsup \frac{\sqrt{a_{n+1}}}{\sqrt{a_{n}}} = \sqrt{limsup \frac{a_{n+1}}{a_{n}}}$ ?

I think this is true for normal limits but does it extend to limsup?

 

[mathman]

As long as the a's don't go negative, and stay real, you're OK.