@Kitonum 

This is exactly what I needed! Thank you so much for explaining it to me.

@nm 

Thank you for the response! I should have mentioned that I wasn't allowed to use any built in Fourier functions.... hindsight is 20/20. Sorry about that.

I did figure out how to do it in the end, 

http://vnatsci.ltu.edu/s_schneider/courses/maple/fourier/seq_square.shtml

This was a very helpful source for anyone else who might be interested.

I changed my code slightly, same issue though:

with (plots):

L := [seq(5*2^i, i = 0 .. 7)];

[5, 10, 20, 40, 80, 160, 320, 640]

animate( plot, [2/((2*n-1)*Pi))*sin((2*n-1)*Pi*x], n=L);
Error, `)` unexpected