Answer
The sequence $c_n$ converges to $ 1.$
Work Step by Step
We have
$$\lim_{n\to \infty}c_n=\lim_{n\to \infty}
\frac{n}{n+n^{1 / n}}
\\
= \lim_{n\to \infty}
\frac{1}{1+n^{\frac{1}{n}-1}}
= 1
.$$
Hence, by Theorem 1, the sequence $c_n$ converges to $ 1.$
