Our book denotes the Weierstrass M-Test as :
Let $M_n > 0$ be a real number satisfying $|f_n(x)| \leq M_n$. If $\sum M_n$ converges, then $\sum f_n$ converges uniformly on A.
Is the M chosen in the test presumed to be a constant for all terms, or a sequence of constants? Because I know if the M is a constant the entire time, I can use that it is Cauchy and prove the test relatively simply.
$M_n$ is a sequence dependent on $n$ bounding $f_n(x)$ for all $n \in \mathbb{N}$ so $M_n$ can be a constant sequence as long as it can bound $f_n(x)$.