Uniform and absolutely convergence of functions

Question

Is there any relationship between absolutely convergence and uniform convergence of function . I know a sequence of function which converge uniformly but not absolutely . Please provide example or proof of converse part.

Answer 1

$\sum_{n=0}^\infty \frac{1}{n^2-x}$ converges absolutely for any $x\notin\mathbb{Z}$ but clearly diverges whenever $x$ approaches an integer, so it could not possibly converge uniformly.