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What is the error in this computation?

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Muhammad Usman
Muhammad Usman 2020-1-4
评论： Walter Roberson 2020-1-4
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

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采纳的回答

Walter Roberson
Walter Roberson 2020-1-4
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 个评论
显示 1更早的评论
Steven Lord
Steven Lord 2020-1-4
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
Walter Roberson 2020-1-4
Using k=1:2:16 should duplicate your manual calculation.

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