Answer
Converges
Work Step by Step
Let $u_n=\dfrac{n-1}{n^4+2}$
When the numerator increases, the value of fraction is always increasing and also, when the denominator decreases, the value of fraction is always increasing.
$\implies \dfrac{n}{n^4+2} \leq \dfrac{n}{n^4}=\dfrac{1}{n^3}$
so, $u_n \leq \dfrac{1}{n^3}$
Here, $\Sigma_{n=1}^\infty \dfrac{1}{n^3}$ converges by the p-series with $p=3$.
Hence, the series converges by The Comparison Test.