1. Why are all of the even coefficients zero in the analysis on the previous page?
  2. Suppose you had a square wave that looked like the one below. Make a Fourier series (of at least three terms) to approximate it. You'll soon see that sines don't help. Why not?
  3. Look at the square wave function written in summation notation on the first page. Explain where the (2k + 1) terms come from.
  4. In the Fourier series for the square wave, the coefficient decreased (in this case, from 1 to 1/3 to 1/5) as we added more terms. That's typical of Fourier series in general. Why do you think Fourier coefficients tend to get smaller the further you get in the series?
  5. Try building up
    What shape will it have when you carry the series out to infinity?

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