After reading your post, I took a quick look, but did not come across any series that matched this one.
Regardless, unless I made a mistake, the only relevant part of the question is pretty much worded as I stated it in my original post: "Sketch the graph to which the Fourier series converges."
The original problem is this:
for all x
It is a saw tooth waveform going from at to at and from at to at , then repeats ...
Note there appears to be a mistake somewhere, that series does not correspond to that function.
I know how to sketch the curve of the initial set of equations. What I don't know is how to sketch the graph to which the resulting Fourier series converges.
I went over my work again, and I can't find any mistake. I'll show the major steps:
If you have done the working correct it will converge to the original function. If you are going to plot the partial sums you will need some computational system to do the calculations for any thing other than two or three terms.
Thank you for pointing that out! I completely missed that part of the technique when it was discussed.
Okay, so now that I've made that correction and redone everything, I now get this:
Looking at that, doesn't that just converge to zero?