infinite series for pi

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AngelsaAtWar
AngelsaAtWar 2013-2-2
Hi I am trying to create an infinite series for pi using INF SIGMA http://mathworld.wolfram.com/images/equations/PiFormulas/NumberedEquation14.gif
I am having a hard time figuring out how to even start this....
i have tried.....
value=0;
k=1;
for k=1:3;
if k<=3;
value= .0625^k
n=n+1;
end
end
for the first part but it says "unexpected expression error". I have to have it go up to 20 terms from 0. Can someone please help me with this. I am new to MATLAB and having a hard time doing this series. Thank You. This is the student version of MATLAB
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per isakson
per isakson 2013-2-3
编辑：per isakson 2013-2-3
I cannot reproduce the error you see. A couple of comments
  • k = 1; -- has no effect
  • n = n+1; -- n must have an initial value
  • value is a scalar that stores the last value, i.e (1/16)^3
  • "n's to k's at (n=n+1)" -- do not assign values to the loop counter
Walter Roberson
Walter Roberson 2013-2-3
When you try, what is the shortest part that produces the unexpected expression error? Does it say which line it is occurring on? Does it print out the line with a vertical bar under one of the characters? If it does then it is saying that character begins the unexpected one.
What character set are you using?

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Image Analyst
Image Analyst 2013-2-3
Hint:
theSum = 0.0;
r = -41.2; % I have no idea what r is supposed to be.
% Plug in the correct value for r.
for k = 1 : 14 % or whatever k you want to stop at
term1 = (4 + 8*r) / (8*k + 1);
term2 = -8*r / (8*k+2);
term3 = -4*r / (8*k+3);
term4 = -(2+8*r) / (8*k+4);
term5 = -(1+2*r) / (8*k+5);
term6 = -(1+2*r) / (8*k+6);
term7 = r / (8*k+7);
term8 = (1/16)^k;
thisSum = (term1+term2+term3+term4+term5+term6+term7)*term8;
theSum = theSum + thisSum
end
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Image Analyst
Image Analyst 2013-2-3
Your shorter version works with no error, though the k=k+1 line is useless. What do you think the "for" line does? It iterates over k, so why are you trying to increment k yourself? Also, you didn't say what the theoretical value for r should be.
AngelsaAtWar
AngelsaAtWar 2013-2-4
the theoretical value apparently was 0 for r and thnk you so much for your help it did work!!! God bless you and sorry that I am new to all this stuff!

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Richard Zapor
Richard Zapor 2013-2-3
Vectorization and output
%AngelsaAtWar
%http://mathworld.wolfram.com/PiFormulas.html
% The ./ and .^ are needed for the vectorization
ferguson=@(r,k)( (4+8*r)./(8*k+1)-8*r./(8*k+2)-4*r./(8*k+3)-(2+8*r)./(8*k+4) -...
(1+2*r)./(8*k+5)-(1+2*r)./(8*k+6)+r./(8*k+7) )./16.^k;
r=0;
kmax=19; % Twenty terms including the zeroth
terms=ferguson(r,0:kmax);
pi_approx=sum(terms);
fprintf('%.8g\n',terms)
fprintf('Pi approx %.8g\n',pi_approx)

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