Series converge or diverge : $\sum^\infty_{n=1}n(1+n^2)^p$ , $p\in\mathbb{R}$? 
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*$\sum^\infty_{n=1}n(1+n^2)^p$ , $p\in\mathbb{R}$


I tried to compare it with other known sequencies but i couldn't find the right one.
I also tried to solve it using Mathematical Induction (for p=-1) but it led me nowhere.
Any suggestions about what should I do?

Notice how $n^2+1$ is asymtopical to $n^2$. Then, your series will behave like $n^{1+2p}=\dfrac{1}{n^{-2p-1}}$. Can you compare this to a known series?
