MATLAB: How to make a function that calculate appoximate value of pi

homeworkpiseriessum

Hi every one; I am going to make a function called a_pi that uses the following approximations of pi

http://www.mathworks.com/matlabcentral/answers/uploaded_files/31727/pi_appoximate.jpg

but that function should have following specifications Instead of going to infinity, the function stops at the smallest k for which the approximation differs from pi (i.e., the value returned MATLAB’s built-‐in function) by no more than the positive scalar, delta, which is the only input argument. The first output of the function is the approximate value of π, while the second is k. (Note: if your program or the grader takes a long time, you may have created an infinite loop and need to hit Ctrl-‐C on your keyboard.) How to deal with that question.Thanks in advance for assistance..

Best Answer

function [pi_here,k1] = a_pi(delta)
    f = @(k)sqrt(12)* 1./(  (2*k+1).*(-3).^k  )  ;
    k1 = ceil(fzero(@(k)abs(f(k)) - delta,1)); 
    pi_here = sum(f(0:k1));
end

function [pi_here,k1] = a_pi(delta)
    f = @(k)sqrt(12)* sum(1./(  (2*k+1).*(-3).^k  ))  ;
    k1 = ceil(fzero(@(k)abs(f(0:k) - pi) - delta,1)); 
    pi_here = f(0:k1);
end

function [pi_here,k1] = a_pi(delta)
    k = 0;
    pi_here = 0;
    while  abs(pi_here - pi) > delta
        pi_here = pi_here +  sqrt(12)./(  (2*k+1).*(-3).^k  );
        k = k + 1;
    end
    k1= k - 1;
end

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l = 1;
B = [0.0250; 0.0500; 0.0750; 0.1000; 0.1250; 0.1500; 0.1750; 0.2000; 0.2250; 0.2500; 0.2750; 0.3000; 0.3250; 0.3500; 0.3750; 0.4000];
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Best Answer

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