If $0 \leq f_n(x)\leq g_n(x)$ and $\Sigma_{n=1}^{\infty}g(n)$ converges uniformly, then $\Sigma_{n=1}^{\infty}f(n)$ converges uniformly?

Question

I am pretty sure this has to be true. I go back to basic sequence and series, if $0 \leq (a_k) \leq (b_k)$, I know that if $\Sigma_{k=1}^{\infty}(b_k)$ converges, then $\Sigma_{k=1}^{\infty}(a_k)$ converges.

Then I just need to apply the Weierstrass M-test to the series of functions, right?

Thanks!