Determining pointwise convergence

Question

Let $$f_{n}(x)=\frac{1-nx^2}{(1+nx^2)^2}.$$

Am I right in saying that $f_{n}(x)\not\rightarrow 0$ as $f_n(0)=1$ for all $n$?

Answer 1

Yes, the limit of the sequence $a_n = 1$ for all $n$ is $1$. So whatever $\lim_{n\rightarrow \infty} f_n$ is, it is $1$ at zero.