Determining Divergence or Convergence in Series

[badirishluck]

Homework Statement

\sum (2n^{2}+3n)/\sqrt{5+n^{5}}
index n=1 to infinity

Homework Equations

The Attempt at a Solution

I tried both the Ratio Test (limit as n goes to infinity of a_{n+1}/a_{n}) and the Limit comparison test (limit as n goes to infinity of a_{n}/ b_{n}) but wasn't able to come up with the same answer from the two tests. What am I doing wrong?
Does it converge or diverge? How?

 

[LogicalTime]

try breaking it into 2 pieces and see what you can do with the individual pieces, see if
\sum (2n^{2})/\sqrt{5+n^{5}}
converges, if it does then the whole thing does since the 2nd term is smaller, if it doesn't then the whole thing does not converge.