Answer
Converges
Work Step by Step
The given series can be summed up as: $\dfrac{1}{3}+\dfrac{1}{8}+\dfrac{1}{15}+.....=\Sigma_{n=1}^{\infty} \dfrac{1}{n(n+2)}$
We can see that the degree of the denominator is equal to $k=2$ and the degree of the numerator is equal to $j=0$.
This implies that $j \lt k$
Also, the condition $ j=0 \lt k-1=1$ has been satisfied.
Hence, we can conclude that the given series converges.