How do I program to calculate the estimate of pi using Leibniz but enabling me to select number n?

I need to program the estimate for pi using Leibniz summation but I want to choose number of n myself, rather than make an infinite loop. What is pi when n=4, n=13 etc. Can someone please explain how I can do that? I'm struggling

Answer 1

[Star Strider]

You don’t need a loop. You can take advantage of MATLAB’s vectorised operations:

N = 10;                                                 % Number Of Terms
pi4 = 1./(1:2:N) .* -(-1).^(1:fix(N/2));                % Series
cs_pi = 4*cumsum(pi4);                                  % Term-Wise Cumulative Sum
s_pi = 4*sum(pi4);                                      % Sum

By setting ‘N’ to as many terms as you want, you can see the series, term-wise cumulative sum, and sum. I multiplied it by 4 to see the approximations to pi. Experiment with it!