Evaluating the liminf and limsup

Question

So I am a little bit stuck on finding the liminf and limsup of the following interval:

$$[(-1/n)^{n} , 2]$$

I know that

$$\liminf_{n\to\infty} A_n = \cup^{\infty}_{n=1}(\cap^{\infty}_{j=n}A_{j})$$ $$\limsup_{n\to\infty} A_n = \cap^{\infty}_{n=1}(\cup^{\infty}_{j=n}A_{j})$$

but I do not know how to use this information to solve the question.

-Thanks!

Answer 1

HINT

Note that $ |a_n|= |(-1/n)^n|\to 0$ is strictly decreasing thus

$$-1\le a_n\le \frac14$$