# Question about algebraic rule for limsup

1. Oct 22, 2011

### 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?

2. Oct 22, 2011

### mathman

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