What is the error in this computation?

Here I want to plot a simple sum.

I computed it manually by iterating different values, and then did it same by using for loop, but there is some mistake, can somebody figure it out for me.

Below given is my code:

x = 0:pi/16:pi;
 s = (8/(pi*(1^3)))*sin(1*x)+...
     (8/(pi*(3^3)))*sin(3*x)+...
     (8/(pi*(5^3)))*sin(5*x)+...
     (8/(pi*(7^3)))*sin(7*x)+...
     (8/(pi*(9^3)))*sin(9*x)+...
     (8/(pi*(11^3)))*sin(11*x)+...
     (8/(pi*(13^3)))*sin(13*x)+...
     (8/(pi*(15^3)))*sin(15*x);
 ss = 0;
 for k =1:16
     ss = ss + (8/(pi*(k^3)))*sin(k*x);
 end
 plot(x,s,'b-',x,ss,'r-');
 

Why I choose odd values in manual sum because sin(k*pi) = 0, where k=2,4,... ,but i took all (even and odd) values in for loop

The plot generated is given below:

Answer 1

[Walter Roberson]

sin(k*pi) is 0 for integer k but you have sin(k*x) where x is a fraction of pi and that does not vanish.

[Muhammad Usman]

Got it.

Please suggest me to improve my loop to get the desied result (compiute manually)

Thanks

[Steven Lord]

In theory sin(k*pi) is 0 for integer k. In practice if you're computing sin(k*pi) consider using the sinpi function introduced in release R2018b.

sin(pi) % not exactly 0
sinpi(1) % exactly 0

[Walter Roberson]

Using k=1:2:16 should duplicate your manual calculation.