The Gregory series(http://mathworld.wolfram.com/GregorySeries.html) is one formu

Question

The Gregory series(http://mathworld.wolfram.com/GregorySeries.html) is one formula for computing pi/4 (multiply by 4 to get pi). Define error as the magnitude of the difference between the sum containing N terms and the true value of pi. Write a script which prompts the user for an error value, uses a loop to determine how many terms in the sum are necessary to achieve that error value, and prints the pi approximation, actual error, and number of terms. Test the script using error values of: 10-2, 10-4, and (if possible) 10-6

Explanation / Answer

clear all
clc
abs_err=10^-4 ;%Place all your error terms here;
pi_calc=0;
err=1;
k=0;
while (err > abs_err)
k=k+1;
pi_calc=pi_calc+(-1)^(k+1)/(2*k-1);
err=abs(pi-pi_calc*4);
end
k
err

Result for err=0.0001

k =

10000

err =

9.999999975862650e-05

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