What Role Do Ck and k=1 Play in Fourier Series?

[Whoohw]

Homework Statement

Consider the following equation for the Fourier series:
f(t) = SUM k=1->infinity (Ck * sin(k*pi*t)

What is the meaning of the Ck terms?
What is the importance of the K=1 term?

Homework Equations

The Attempt at a Solution

Ck = Fourier Coefficents. They are the amplitudes of each term of the series, they will determine the shape of the final wave?

The k = 1 term is the "DC" or constant/mean of the series?

 

[jbunniii]

The k=1 term is clearly not the constant/mean, because it is associated with $\sin(\pi t)$. The k=0 term is the constant/mean. In your case the k=0 term is 0.

 

[Whoohw]

I'm lost as to what the significance of the n=1 term could be over any other term then, other than the most dominant?

 

[jbunniii]

The k=1 term is the so-called "fundamental":

http://en.wikipedia.org/wiki/Fundamental_frequency

Aside from that, I don't know what the question's author is looking for.

It is not necessarily the most dominant; in fact, there's nothing preventing $C_1 = 0$.