To elaborate more, when we say that a signal is the linear combination of infinitely many frequencies, if those frequencies are multiples of a fundamental frequency (that is, a countable set of frequencies), then we are talking about a Fourier series and the signal must be periodic

But if those frequencies span a whole continuum (rather than frequencies f, 2f, 3f, 4f..), that is, an uncountable set of frequencies, then this signal is non-periodic and we can't talk about a Fourier series anymore, we must use the Fourier transform