Conclusions about convergence of series

From the series solution of a differential equation, I obtained the following recurrence relation:
$a_{j+2}=a_j \left(\frac{(j+1)(j+3)-n(n+2)}{(j+2)(j+3)}\right),$ where $n$ is some constant. $\\$
From the ratio test we get the limit of the ratio of successive terms as 1 as j tends to infinity. How can we conclude the convergence or divergence of such a series?
The answer says that the series with the above coefficients diverges for x=1.

Thanks for the help in advance.