Can You Determine \(a_0\) in Fourier Series by Plugging \(n=0\) into \(a_n\)?

[jbrussell93]

I'm having trouble finding a definite answer to this question: When finding the Fourier series of a function is it always possible to find $a_0$ by first finding $a_n$ and just plugging in $n=0$?

 

[TSny]

To help answer this, suppose you had two periodic functions f(x) and g(x) with f(x) = g(x) + C where C is a constant. How would the coefficient $a_0$ compare for the two functions? How would the coefficients $a_n$ for $n \neq 0$ compare for the two functions?