First off, sorry if this is in the wrong section.

The question goes...

We define a sequence by $\displaystyle x_{n}=\cos{(n\pi/3)}$. Find an increasing list of numbers $\displaystyle 1\leq n_{1}<n_{2}<n_{3}<...$, so that the subsequence $\displaystyle y_{k}=x_{n_{k}}$ tends to 1. Prove that $\displaystyle \{x_{n}\}_{n=1}^{\infty}$ does not tend to a limit.

I have no clue. I hate stuff like this.