**Problem**: Let $a\_n=\frac{1}{n^2}$. It converges to $0$. Proof that it converges to $0$

**Proof**: Let $\epsilon>0$ be given. Let $N=\left \lceil \frac{1}{\sqrt{\epsilon}} \right \rceil$. For $n>N$ we have that

$$ |\frac{1}{n^2}-0|$$
$$= \frac{1}{n^2}$$
$$<\frac{1}{N^2} $$
$$ \leq 1/(1/\sqrt{\epsilon})^2$$
$$=\epsilon$$

Q.E.D

**Questions**

* What is the sratchwork done to find such a $N$? (Normally I woudl see it by the calculations)
* Why use the ceiling function?