In the mentioned homework, part of the solution involves finding the Fourier coefficients of the triangle wave.
The solution mentions that we can express this function as follows:
What does that multiplication signal means?
I approached the problem from a completely different angle of viewing the triangle wave as the integral of a piecewise constant function defined as follows:
$ f(x)= \begin{cases} \frac{1}{2}&\text{if}\, -\frac{1}{4}\leq x\leq0\\ -\frac{1}{2}&\text{if}\, 0\leq x\leq\frac{1}{4} \end{cases} $
Taking the integral similarly and then multiplying by $\frac{1}{2\pi ik}$ gives me a completely different answer of $-\frac{1}{4\pi^2k^2}[\cos(\frac{\pi}{2}k)-1]$.
What is wrong with my approach?