I am working with a definition of a divergent limit as follows:
A sequence $\{a_n\}$ diverges to $-\infty$ if, given any number $M$, there is an $N$ so that $n \ge N$ implies that $a_n \le M$.
The sequence I am considering is $a_n = -n^2$, which I thought would be pretty simple, but I keep running into a snag.
My Work:
For a given $M$, we want to show that $n \ge N \Rightarrow -n^2 \le M$. So $n^2 \ge -M$. But here is where I run into trouble, because I can't take square roots from here. What should I do?