Diverging sequence I can't understand diverging sequences. How can I prove that $a_n=1/n^2-\sqrt{n}$ is divering? Where to start? What picture should I have in my mind? I tried to use $\exists z \forall n^* \exists n\ge n^*: |a_n-A|\ge z$, but how should I see this? And how can I solve the question with this property?

Now I got this:
$|a_n-A| \ge \epsilon$
$\frac{1}{n^2} - sqrt(n) \ge \epsilon + |A|$
Suppose $u=sqrt(n) (u \ge 0)$
$u^{-4}-u \ge \epsilon + |A|$
$u^{-4} \ge u^{-4} - u$
$u^{-4} \ge \epsilon + |A|$
$u \ge (\epsilon + |A|)^\frac{-1}{4}$
$n \ge \frac{1}{sqrt(\epsilon + |A|)}$
And what may I conclude now?
