Write a matlab function for approximating the value of pi (certain equation)

Hi.

Task:

Write a program that calculates the approximation of pi when it is given an upper limit of the sum 𝑁.

Code that I'm trying to use:

function p = fun_my(n)

p = 0;

for k = 1:n

p = p + sqrt(8 + sum(16./((2*(1:n) - 1).^2 .* (2*(1:n) + 1).^2)));

end

Thanks for advance!

Answer 1

[Torsten]

You sum twice.

And

(2*n-1)^2*(2*n+1)^2 = (4*n^2-1)^2

Either use

n = 20;
p = 0;
for k = 1:n
    p = p + 1/(4*k^2-1)^2;
end
p = sqrt(8 + 16*p)

p = 3.1416

or use

n = 20;
p = sum(1./(4*(1:n).^2-1).^2);
p = sqrt(8+16*p)

p = 3.1416