= Solution
{c}
The <Weierstrass M-test> states: if <functions> $f_n:E\to\mathbb R$ or $\mathbb C$ satisfy
$$
|f_n(x)|\leq M_n\quad\text{for every }x\in E,
\qquad M_n\geq0,
\qquad\sum_{n=1}^{\infty}M_n<\infty,
$$
then $\sum f_n$ has <uniform convergence> and <absolute convergence> on $E$. In fact $\sum|f_n|$ also has <uniform convergence>, since every tail is bounded by the corresponding tail of $\sum M_n$:
$$
\boxed{\sup_{x\in E}\sum_{n=N+1}^{\infty}|f_n(x)|\leq\sum_{n=N+1}^{\infty}M_n\longrightarrow0.}
$$
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