What is the error in this computation?
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Muhammad Usman
on 4 Jan 2020
Commented: Walter Roberson
on 4 Jan 2020
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:
![123.bmp](https://www.mathworks.com/matlabcentral/answers/uploaded_files/259720/123.bmp)
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Accepted Answer
Walter Roberson
on 4 Jan 2020
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.
3 Comments
Steven Lord
on 4 Jan 2020
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
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