Problem 1. Discuss the convergence and the uniform convergence of the series $\sum f_n$, where
$f_n(x)$ is given by:
(a) $(x^2 + n^2)^{-1}$,
(b) $(nx)^{-2}$ ($x \neq 0$),
(c) $\sin(x/n^2)$,
(d) $(x^n + 1)^{-1}$ ($x \neq 0$),
(e) $x^n / (x^n + 1)$ ($x \geq 0$).
