How to reconstruct a square signal by determining the Complex Fourier Coefficients and using those N coefficients in exponential form?

I want to determine the Fourier Series Complex Coefficients of the signal x(t), based on the below formula and to plot the amplitude spectre.

Also, I want to rebuild the initial signal using the determined Fourier Coefficients, and I want to plot on the same graph the initial signal and the rebuild one so that I can compare them. Unfortunately, haven't got the expecte results. Formula for the rebuilt signal:

%My code:
%Type of signal: square

T = 40; %Period of the signal [s]

F=1/T;   % fr

D = 23; % length of signal(duration)
dt=(D/T)*100;
N = 50; %Number of coefficients


w0 = 2*pi/T; %signal pulse


t1= 0:0.002:T; % original signal sampling

x1 = square((2*pi*F)*(t1),dt);%initial square signal

t2= 0:0.002:D; %modified signal sampling

x2 = zeros(1,length(t2)); %initializing the modified signal with null values.
dif=T-D;

x2(t1<=D)=x1(t1<=D);% modify the null values with values from the original signal.
x2(1,dif:D)=x2(1,dif:D); %modify for values of t1>=T-D.
x2(t1>=T-D)=x1; 

subplot(2,1,1)
plot(t2,x2),title('x(t)+ reconstructed signal)');
hold on




for k = -N:N %k represents the variable after which the sum is achieved

    
x3 = x1; %x3 represents the signal obtained after the Fourier Series formula;

    
x3 = x3 .* exp(-1i*k*w0*t1); 
    
X(k+N+1) = 0; %initialise with null value

end

    
for i = 1:length(t1)-1


     
X(k+N+1) = X(k+N+1) + (t1(i+1)-t1(i)) * (x3(i)+x3(i+1))/2; %reconstruction using the coefficients


    
 
end


for i = 1:length(t1) 

    
x_rec(i) = 0; %initialise with null value


% x_rec is the reconstructed signal using N Coefficients
end

for k=-N:N

        
x_rec(i) = x_rec(i) + (1/T) * X(k+51) * exp(1i*k*w0*t1(i));  %reconstruction using the coefficients ( the integral being calculated as a sum)



end

plot( t1, x_rec, '--') 
subplot(2,1,2)
w=-50*w0:w0:50*w0; %w is the vector which allows displaying the spectre of the function

stem(w/(2*pi),abs(X));

My result: