Answer
Diverges.
Work Step by Step
We have
$$ \lim\limits_{n \to \infty}{c_n}=\lim\limits_{n \to \infty} 1.01^n=\infty.$$
Where we used the fact that $\lim_{x\to \infty } a^x=\infty$ when $|a|\gt 1$. Using Theorem 1, we see that the sequence $c_n$ diverges.
