We will study the convergence of the series
[tex]\sum_{n=1}^{\infty}(1+n^2)^p[/tex]
For [tex]p=0[/tex] the series has constant general term which is divergent.
For [tex]p \geq 0[/tex] the series diverges since its general term goes to infinity as n goes to infinity.
For [tex]p < 0[/tex], the series converges since it is equivalent to the Riemann series.
