Question:

Give an example of a divergent sequence $\displaystyle (a_n)_{n\in\mathbb{N}} $ that satisfies the following conditions:

(i) For every $\displaystyle \epsilon >0$, there exists an $\displaystyle X$ such that for infinitely many $\displaystyle x>X$,

$\displaystyle \left| a_n - 3 \right| < \epsilon $

(ii) There exists an $\displaystyle \epsilon >0$ and a $\displaystyle X \in\mathbb{N} $ such that for all $\displaystyle x>X $,

$\displaystyle \left| a_n - 3 \right| < \epsilon $

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I have absolutely no idea how to do these For the infinitely many x>X one, I'm thinking this could involve a trig function since it doesn't converge and repeats every $\displaystyle 2\pi $. Please help.