Find the Fourier coefficients of the "mountains" function

This project must be done by individuals.

An electronic chip produces a voltage which shows brief positive "beeps", separated by stretches of time during which the voltage is zero.

A graph showing just one cycle of this periodic variation is shown below.

Your job is to find the first few Fourier components of this function. In particular,

n = 0: A₀, B₀
n = 1: A₁, B₁
n = 2: A₂, B₂

Compute these coefficients.

Use these coefficients to compute the value of the Fourier series over the range t = 0 to t = 4. Make a graph of the sum of the terms over this range. How well does it match the input function?

Hand in sheet(s) of paper, showing all your work. If you decide to use a computer or calculator to do some of the work, provide screenshots or printouts describing your technique.