Exercise 105

Let $$f(t) = \nicefrac{t}{2} \qquad \text{for } \; {-\pi} < t < \pi$$ extended periodically.

1. Compute the Fourier series for $f(t)$.
2. Plug in $t=\nicefrac{\pi}{2}$ to find a series representation for $\nicefrac{\pi}{4}$.
3. Using the first 4 terms of the result from part b) approximate $\nicefrac{\pi}{4}$.