I will assume that you're asking about $\limsup$ and $\liminf$. (This is, in my opinion the only reasonable explanation.)
Peter suggested in his comment that you could have a look at the subsequences:
From the above you should have some inequalities for the values of $\liminf a_n$ and $\limsup a_n$, if you are able to prove the opposite inequalities, you're done. So for this part: Are you able to show that for each $n$ you have $-\frac1n\le a_n \le 1+\frac1n$? What do these inequalities tell you about $\liminf a_n$ and $\limsup a_n$?