Answer
Converges
Work Step by Step
Consider $a_n=\dfrac{n-1}{n^4+2}$
When we increase the numerator, the value of the fraction will always increase and when we decrease the denominator, the value of the fraction will also always increase.
Thus, $\dfrac{n}{n^4+2} \leq \dfrac{n}{n^4}=\dfrac{1}{n^3}$
we get $a_n \leq \dfrac{1}{n^3}$
Here, $\Sigma_{n=1}^\infty \dfrac{1}{n^3},p=3$ converges by the p-series test.
Thus the series converges by the comparison test.
