$P_n(x):R\rightarrow R$ is a sequence of functions defined by: $$P_n(x)= \frac{n}{1+n^2x^2}$$
f:R->C is continuous and 2pi periodic. We define:
$$f_n(x)=\frac{1}{\pi}\int \limits_{-\infty}^{\infty}f(x-t)P_n(t)dt$$
I should prove that $f_n \rightarrow f$ uniformly in $\mathbb R$.
This is an excercise from final test in calculus. My guess is that it is somehow related to Fourier. Can anyone help please?
Idea: $\frac1\pi\frac{n}{1+n^2x^2}$ is an approximation to the identity.