Sum of two Uniform Convergent Functional Series

Let $F(x):=\displatstyle\sum\limits_{j=1}^{\infty}f_{j} (x)$ and
$G(x):=\displatstyle\sum\limits_{j=1}^{\infty}g_{j} (x)$

be uniformly convergent functional series.

Show that $\displatstyle\sum\limits_{j=1}^{\infty}(f_{j} + g_{j})$ is uniformly converget to $F + G$

Now I suppose I need to use the Chebyshev Norm and show that $\bigg\lVert\displatstyle\sum\limits_{j=1}^{\infty} (f_{j} + g_{j}) - (F + G)\bigg\rVert_{\infty} <\epsilon$

Or any other method perhaps??
I have no idea other than that one, any help would be much appriciated thanks