Approximation not falls within the expected range

Here's my script:

     n=1;  
while abs(pi-sum(4./((2*(1:n)-1).*(-1).^((1:n)+1))))>0.001
      n=n+1;    
end
fprintf('The approximation using Leibniz''s formula falls within 0,001 of pi when it equals to\n')
fprintf('%.9f with n equls %d\n\n',sum(4./((2*(1:n)-1).*(-1).^((1:n)+1))),n)
    end

As shown, I try to make the result falls within 0.001 of pi, however, I get n=1000 an approximation equals 3.140592654.

My friend gets n=2002, so is mine wrong?

Thank you!

Answer 1

[ag]

Hi Zhuoying,

I kindly suggest you to refer the following MathWorks file exchange page, which demonstrates implementation of the Leibniz formula: Approximation of Pi - https://www.mathworks.com/matlabcentral/fileexchange/102659-approximation-of-pi-leibniz-formula

You can find the code on the "Functions" tab.

Hope this helps!