Fourier series for square wave

Question

Could I get some assistance with this? Not sure how to get the solution at all. See image attached.

Answer 1

For the Fourier series of the function $f(x)$: $$f(x)=\frac{\text{a}_0}{2}+\sum_{n=1}^\infty\text{a}_\text{n}\cos\left(\text{n}x\right)+\sum_{n=1}^\infty\text{b}_\text{n}\sin\left(\text{n}x\right)\tag1$$

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1. For $\text{a}_0$ we have: $$\text{a}_0=\frac{1}{\pi}\int_{-\pi}^\pi f(x)\space\text{d}x\tag2$$
2. For $\text{a}_\text{n}$ we have: $$\text{a}_\text{n}=\frac{1}{\pi}\int_{-\pi}^\pi f(x)\cos(\text{n}x)\space\text{d}x\tag3$$
3. For $\text{b}_\text{n}$ we have: $$\text{b}_\text{n}=\frac{1}{\pi}\int_{-\pi}^\pi f(x)\sin(\text{n}x)\space\text{d}x\tag4$$