I'm a little stuck in understanding about why some coefficients in my FS disappear.
I have to build the cos series of |sin(x)|.
After Integrating for $a_n$ I get the following Formula for the Coefficients of $cos(nx)$:
$\dfrac{2}{\pi} \frac{(-1)^n+1}{1-n^2} $
For the FS: $ \dfrac{2}{\pi}+\dfrac{2}{\pi}\sum_{i=2}^{\infty} \frac{(-1)^n+1}{1-n^2} cos(nx) $
Comparing it to Meyberg (see Picture) 
The coefficients are the same. (Even though I don't understand how to get to his formula)
What is giving me a headache is to understand why all odd Coefficients are $0$? I understand 1 is not allowed since it's in the denominator of the formula. (Numerically the integral becomes 0... so it applies too)
In his explanation on the book, the only says for symmetric functions (odd or even functions) half of the coefficients disappear but in another exercise (Calculating FS of $x\cdot cos(x)$) all of the coefficients are present. Could someone please enlighten me?
Cheers, Santiago