I plan to solve the following exercise
given $\epsilon>0$, calculate $m_\epsilon \in \mathbb{N}$ such that for all $n \ge m_\epsilon$ it is verified that $|x_n-x|<\epsilon$, in this case you have to
$x_n= n^{2}a^{n}$ and $x=0$, also $|a|<1$
Well, consider that $$0 \le x_n=|x_n-0|=|n^{2}a^{n}|< \epsilon$$
From where
$$|a^{n}|<\frac{\epsilon}{n^{2}}$$
I have been able to find that, however I have not been able to find the value of $m_\epsilon$.Any help please?