I am currently studying Fourier Analysis on my own. In the Notes I use the following comment is made, which I unfortunately don't understand:
Given that we know the series
$f(x) = \sum c_k e^{ikx}$
converges pointwise (where the $c_k$ are the Fourier coefficients and $f$ is a periodic function), to show uniform convergence it is enough to show that
$ \sum |c_k| < \infty $
I tried to find the result regarding uniform convergence that this comment refers to but so far I wasn't successful.
Could somebody help me and give a hint as to why this is true ? Many thanks!