Show that the sequence converges to 0 under any norm in the space (R,‖.‖)

Question

Show that the sequence $a_n = 1/n^2$ converges to 0 under any norm in the space $(\mathbb{R},\left\| \cdot \right\|)$.

Answer 1

Or more in fundamental calculus, because $\Bbb R$ is not bounded then for every $ε>0$

there exists a $n_0 \in \Bbb N:1/n_0<ε$.Then for every $n>n_0=>n^2>n_0$ we have $\lVert 1/n^2 \rVert <\lVert 1/n_0\rVert<ε$.