Limit of a infinite series $$\frac{2}{2} + \frac{2\cdot 5}{2\cdot 9} + \frac{2\cdot 5\cdot 10}{2\cdot 9\cdot 28} + \cdots + \frac{2\cdot 5\cdot 10 \cdots (n^2+1)}{2\cdot 9\cdot 28\cdots (n^3+1)}\tag1$$
For this series $(1)$, how would one go about applying the comparison test to check for convergence or divergence?

The general term of the series, $a_n$ is given by 
$$a_n=\prod_{k=1}^n\frac{(k^2+1)}{(k^3+1)}$$
Then, we see that
$$\frac{a_{n+1}}{a_n}=\frac{(n+1)^2+1}{(n+1)^3+1}\to 0\implies \text{the series converges}$$
