How to prove that for $f:\mathbb R\rightarrow \mathbb R$ a continuous function, and $(f_n)$ a sequence of functions such that
$$f_n(x) = f(x + 1/n), \forall n \in \mathbb N$$ converges uniformly in every interval $[a,b]$.
Note: I'm looking for ideas on which law or theory to use and not for full solution.
Until now, I have tried to prove that with the definition of uniform convergence using epsilon but that doesn't work here.
Edit:
I need to prove that for every epsilon>0 There in N so that for every n,m>N:$$|fn(x)-fm(x)| < epsilon$$
But from what I'm given that seems impossible to be proven