Suppose $\displaystyle \{f_n\}$ is a sequence of functions converging uniformly to$\displaystyle f$. Define $\displaystyle g_n(x)=f_n\left(x+\frac{1}{n}\right)$ . Show that the sequence $\displaystyle \{g_n\}$ converges pointwise to f.

So I need to show that $\displaystyle f(x)=\lim \limits_{x \to \infty} g_n(x)=\lim \limits_{x \to \infty} f_n\left(x+\frac{1}{n}\right)$

Thanks in advance