Convergence of a series with a parameter by the root test

For $c\in\mathbb R$, let the sequence $\{u_n\}_{n\ge1}$ be defined by

$$u_n=\frac{\left(1+\frac cn\right)^{n^2}}{\left(3-\frac1n\right)^n}.$$

Then the values of $c$ for which the series $\sum_{n=1}^\infty u_n$ converges are