A question on Fourier Series and the frequency of the sinusoids
A function that is not periodic doesn't have a Fourier series. What you can do is take a finite length interval and construct a Fourier series which approximates the function in that interval (and continues it periodically outside that interval).
The sum of several sinusoids with one of the sinusoids having (fundamental) period $T$ can never have a period less than $T$, simply because that one sinusoid will destroy periodicity (with period $&lt;T$) due to its larger period.