Now it is your turn to explore the effect of the varied terms in the series...

Try adding more terms to both Fourier series and observe which one gets you a better approximation to the original function.

I strongly recommend that you use at least the references I provide you with on top of the Mathematica "Help" package to get a better grasp of the process.

The topic of Fourier series is covered in many Mathematics, Physics and Engineering books. Check out at least one. A particularly good one, available in the Cornell library, is Arfken, G. "Fourier Series." Ch. 14 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 760-793, 1985.

While I expect you to understand integration techniques as well as possible, since integrals for the Fourier coefficients can get really tough sometimes, I suggest that you use the convenient online integration tool provided by Wolfram.