Answer
Diverges
Work Step by Step
We are given the series as: $\Sigma_{n=1}^{\infty} \dfrac{n^2}{n^3+1}$
We can see that the degree of the denominator is equal to $k=3$ and the degree of the numerator is equal to $j=2$.
This implies that $j \gt k$
Also, the condition $ j=2 \geq k-1=2$ has been satisfied.
Hence, we can conclude that the given series diverges.
