Considere a função $g(x)=x-2$ se $x \in [0,2[$ e $g(x)=2-x$ se $x \in [2,4[$. A série de Fourier da extensão periódica de $g$ é:
a) $-1+4 \sum \limits _{k=0}^{\infty} \frac{sen \left((2k+1) \frac{\pi}{2} x \right)}{((2k+1)\pi)^2}$
b) $-2-8 \sum \limits _{k=0}^{\infty} \frac{cos(k \pi x)}{(2k \pi)^2}$
c) $-8 \sum \limits _{k=0}^{\infty} \frac{cos \left((2k+1) \pi x \right)}{((2k+1)\pi)^2}$
d) $-1-8 \sum \limits _{k=0}^{\infty} \frac{cos \left((2k+1) \frac{\pi}{2} x \right)}{((2k+1)\pi)^2}$
e) $-\frac{1}{2}-4 \sum \limits _{k=0}^{\infty} \frac{cos \left((2k+1) \frac{\pi}{2} x \right)}{((2k+1)\pi)^2}$