@vv Thank you very much :-)

@vv Hi, thanks for the answer. I now want to do the same for N=5, and am getting the below graph when plotting. Does that seem right? Thanks

f:=t -> t^2;
a_5 := n -> 5/Pi*int(cos(n*t)*f(t),t=0..2*Pi):
b_5 := n -> 5/Pi*int(sin(n*t)*f(t),t=0..2*Pi):
S_5 := (n,t) -> a_5(0)/2+add(a_5(k)*cos(k*t)+b_5(k)*sin(k*t),k=1..n):
plot([f(t),S_5(8,t)], t=0..2*Pi);

@mmcdara Thank you very much :-)

Sorry for the confusion. I'm merely looking for help on what Maple commands/syntax I need to use to have Maple do the above mentioned tasks. I'm trying to learn how to verify my homework math answers and plot nice graphs :-). Anyways thanks for the extensive answers to the math part of this problem.