limit question for a series: n/ sqrt(1+n^2)

[Opus89]

I'm working on a series problem and I'm trying to apply the nth term test to go ahead and see if the series diverges or not. My problem is the sigma sum from 1 to infinity of n/sqrt(1+n^2). I'm trying to take the limit of this but I can't for the life of me see how and remember how to do limits like these. Any suggestions? Thanks

 

[pka]

\(\displaystyle \frac{n}{{\sqrt {1 + n^2 } }} = \frac{1}{{\sqrt {\frac{1}{{n^2 }} + 1} }}\)