Calculate definite vector values and sum()
k = (1 : N-1) .';
f = @(x) A0/2 + sum(A(k) .* cos(2*pi.*k.*x./P) + B(k) .* sin(2*pi*.k.*x./P),1) + A(N).*cos(2*pi.*N.*x/P)/2
For example A = [1,2,3,4], B = [1,2,3], P = 6, and N = 12
N cannot be greater than one less than length(A) or length(B).
Also, unless you store 
in a separate variable like I used here, then you would need to make adjustments to the code to deal with the question of whether you are using 0-based indexing or 1-based indexing.
in a separate variable like I used here, then you would need to make adjustments to the code to deal with the question of whether you are using 0-based indexing or 1-based indexing. Note: this version of the code is vectorized, provided that x is a row vector.
