# use the for or while looping to the series S=4*[sin(theata)/1 +sin(3thea​ta)/3+sin(​5theata)/5​+.....] ,,in the range 0<theata<pi with error bound of 10^-6..?....please help me to solve this question in the earliest opportunity

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majid on 15 Apr 2013
S=4*[sin(theata)/1 +sin(3theata)/3+sin(5theata)/5+.....]

Youssef Khmou on 15 Apr 2013
Edited: Youssef Khmou on 15 Apr 2013
Try this version :
% theta=0:pi/30:pi;
theta=0:0.01:2*pi;
S=0;
tolerance=1e-6;
n=1;
r=6; % random
counter=1;
while r>tolerance
N1=norm(S);
S=S+sin(n*theta)/n;
N2=norm(S);
r=abs(N2-N1);
n=n+2;
counter=counter+1;
end
plot(theta,S);
axis([0 4 0 1])
grid on
Now it approximates well the rectangle, the number of iterations is saved in the variable 'counter', finish the code with the desired prints .
To conclude you work, there a special name of the infinitesimal waves nears the edges , that phenomenon has a special name , it starts with G.....
majid on 16 Apr 2013
ok thanks so much i'll do my best

### More Answers (2)

Image Analyst on 15 Apr 2013
Hint, have a loop over k and calculate sin(k*theata)/k in the loop. I hope that's not doing too much of your homework for you. You still have to make the loop and sum up the term in the loop into the overall sum and then multiply that by 4.
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Image Analyst on 15 Apr 2013
Use a for loop instead of a while loop. Have an outer for loop over theata.
for theata = 0: 0.01 : pi
Don't use "sum" since that is a built in function name and you'll be destroying it. Use S like you started to. Finally you need to calculate the "true" value (whatever that is) and compare it to S and bail out of your inner for loop once the error is less than 1E-6.

Carlos on 15 Apr 2013
Edited: Carlos on 15 Apr 2013
Try this
theata=pi/2;
a=1;
S=0;
n=1;
while (a>10e-6)
a=sin(n*theata)/n;
S=S+a;
n=n+2;
end
S=4*S;
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Carlos on 15 Apr 2013
Sorry, I misunderstood the question, I thought theata should be a fixed value.