Question

Find the positive values of p for which the series converges. (enter your answer using interval notation.) ∞ n (1 + n2)p n = 1

Answer 1

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