I$\text{'}$m to plot the following signal using matlab using Fourier Series. The frequency is $20$ kHz$.$ Below are the manual calculation for the trigonometric Fourier series done by myself. Below are my Matlab codings. Is my manual calculation have mistake$/$wrong$?$ Or my coding is wrong? Why the matlab gives a graph that is not same with the first picture? How can I get the frequency domain from my manual calculation of x$($t$)?$ Thank you! I would upvote if you give good answer, and vice$-$versa.

My Matlab Codings:

t $=-5$:$0\mathrm{.}01$:$5$;

figure;

Final$\_$x$\_$t $=$ zeros$($size$($t$))$;

for n $=1$:$50$;

Individual$\_$term$\_$of$\_$x$\_$t $=(2/(((2*$ n $+1)*$ pi$)))*$ sin $((2*$ n $+1)*$ t $*40000*$ pi $)$;

Final$\_$x$\_$t $=$ Final$\_$x$\_$t $+$ Individual$\_$term$\_$of$\_$x$\_$t;

end $\%$end the for loop

Final$\_$Final$\_$x$\_$t $=(1/2)+$ Final$\_$x$\_$t

subplot$(4,1,1)$

plot$($t$,$ real$($Final$\_$Final$\_$x$\_$t$))$;

title$(\text{'}$x$($t$)$ for n $=0$ to $5\text{'})$;

xlabel$(\text{'}$Time $($s$)\text{'})$;

ylabel$(\text{'}$Amplitude$\text{'})$;

grid on;