Find the limit of $\frac{1}{n^2(1+x^{2n})}$

Question

Could someone please check if I have the correct solution for this please.

I need to find the limit as n tends to infinity of $$ f_n(x) = \frac{1}{n^2(1+x^{2n})} $$

For $x=0$ we have

$f(0)=1/0$ which is undefined, where do I go from here...

Answer 1

$0 \leq f _n(x) \leq \frac 1 {n^{2}}$. By Squeeze Theorem $\lim_{n\to \infty} f_n(x)=0$ for any real number $x$.