The problems says: By doing an ODD extraction of the function: $$f(x)=\frac{x-\pi}{2}, x \in (0,\pi)$$ calculate the following series: $$ \sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{2n-1}$$
My main problem is that in the exam (2 weeks from now) I've got 30 questions and I suppose that I have to calculate $b_n$ (since it is odd) and after that I should use Parseval's, right?
After calculating $b_n$ I get this (symbolab calculator):
It really takes a long time just to get to the result, but what do I do now with it?
Here are the results if that helps: 
We have that $$ g(x)=\sum_{n\geq 1}\frac{\sin(nx)}{n} \tag{1}$$ is the Fourier series of a sawtooth wave. Over the interval $(0,\pi)$ we have $g(x)=\frac{\pi-x}{2}$,
hence by evaluating both sides of $(1)$ at $x=\frac{\pi}{2}$ it follows that
$$ \frac{\pi}{4}=\sum_{n\geq 1}\frac{\sin(\frac{n\pi}{2})}{n}=\sum_{n\geq 1}\frac{(-1)^{n-1}}{2n-1}\tag{2} $$