Answer
$c_n$ converges to $e^3$.
Work Step by Step
We have
$$
\lim _{n \rightarrow \infty} c_n=\lim _{n\rightarrow \infty}
\left(1+\frac{3}{n}\right)^{n}
\\
=\lim _{n\rightarrow \infty}
\left(1+\frac{1}{n/3}\right)^{n}
=\left(\lim _{n/3\rightarrow \infty}
\left(1+\frac{1}{n/3}\right)^{n/3}\right)^{3}=e^3.
$$
Where we used the fact that $\lim _{m \rightarrow \infty}
\left(1+\frac{1}{m}\right)^{m}=e$.
So, $c_n$ converges to $e^3$.
