infinite series for pi

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

[per isakson]

Try to format the code in the question. It is difficult to see the line breaks. I added

    n = 0;

and now it runs just fine

[AngelsaAtWar]

value = 0 ;

k = 1;

for k = 1 : 3 ;

    if k <= 3;

    value = .0625^k

    n = n + 1;

    end

end

sorry even this does not work for some reason

[AngelsaAtWar]

and I also just switched the n's to k's at (n=n+1)

[per isakson]

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]

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?

Answer 1

[Image Analyst]

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

[AngelsaAtWar]

Hi I tried that with a shorter version of this that I just found and I ended up with this problem.......

theSum = 0.0;
for k = 1 : 21
  term1 = (4) / (8*k + 1);
  term2 = -(2) / (8*k+4);
  term3 = -(1) / (8*k+5);
  term4 = -(1) / (8*k+6);
  term5 = (1/16)^k;
  thisSum = (term1+term2+term3+term4)*term5;
  theSum = theSum + thisSum
    k =k+1 ;
end

all of this ends up with an error saying....Error: Unexpected MATLAB expression.

[Image Analyst]

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]

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!

Answer 2

[Richard Zapor]

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)