Answer
$0$
Work Step by Step
We have
$$\lim_{n\to \infty}c_n=\lim_{n\to \infty}\frac{(-1)^n}{{\sqrt n}}.$$
Since $-1\leq (-1)^n \leq 1$, then $-\frac{1}{\sqrt{n}}\leq \frac{(-1)^n}{\sqrt{n}}\leq \frac{1}{\sqrt{n}}$. Applying the squeeze rule, we find that $$ \lim_{n\to \infty}\frac{(-1)^n}{{\sqrt n}}=0.$$
Hence, by Theorem 1 the sequence $c_n$ converges to $0$.
