How to sketch a graphs for Fourier series coefficients

Question

I'm struggling to plot the correct Fourier series graph for the following function when $n = 1, n = 1.5$ and $n = 2.5.$ $$y = 5 + 20 \sum_{n = 1}^{\infty} \frac{1 - \cos(n \pi)}{\pi^2 n^2}\cdot{\cos(\pi / t)\cdot nt}$$

Answer 1

The fourier coefficients are a function $\mathbb{N} \to \mathbb{C}$ or $\mathbb{N} \to \mathbb{R}$, as in your case. They are not defined for fractional $n$. I suggest you use a bar chart or simply dots at integer evaluation-points.