Answer
Converges
Work Step by Step
Here, we have the given series $\Sigma_{n=1}^{\infty} \dfrac{n}{2n^2+1}$
Next, we will use the nth divergence test for the given series to check whether it is convergent or divergent.
$\lim\limits_{n \to \infty} \dfrac{n}{2n^2+1}=\lim\limits_{n \to \infty} \dfrac{1/n}{2+1/n^2}=\dfrac{0}{2+1/\infty}=0$
Hence, we can conclude that the given series converges by the nth divergence test .
