The Weierstrass M-Test states that if you have a sequence of functions $(f_k)_{k\epsilon\mathbb N}$ where $f_k:A\mapsto\mathbb R$, and suppose that $\forall k \epsilon \mathbb N \exists M_k >0 $ such that
$$|f_k(x)|\leq M_k \forall x \epsilon A$$ and $$\sum_{k=1}^{\infty}M_k <\infty$$
Then the series $\sum_{k}f_k$ converges uniformly on A.
However, the Weierstrass M-test is not applicable to series that converge uniformly but not absolutely.
Therefore, when attempting to prove a series converges uniformly using the M test, do I need to show first of all that the series converges absolutely?