Question

Calculation of the value of pi: The Nilakantha Series was developed in the 15th century as a way to calculate the value of pi: pi = 3 + 4/(2*3*4) -4/(4*5*6) + 4/(6*7*8) -4/(8*9*10)+... . Use a for loop to approximate pi using this technique (5 points). Continue the calculations until the absolute value of the difference between the value of pi stored in MATLAB and the approximation is less than 0.001. Report the appproximation and the number of iterations required (5 points). Hint: to alternate the sign on each term use (-1) raised to a power.

Answer 1

Your Code 1 clc 2 clear all 4 % variable declaration 5 allowed err-0.001; 6 estimated_pi3 10 flag -true; 11 term-0; 12 iter0 13 % looping max 200 iterations 14 for iter 1:200 15 % calculating the pi 16 estimated_pi-estimated_pi term; 17 % checking the flag value to alternate between-and + 18 if flag: true 19 term-4 (num1 num2num3); 20 flag = false; 21 else 22 term-4 (num1 num2 num3); 23 flag -true; 24 end 25 % incrementing the nums 26 num1num1 2; 27 num2 num22; 28 num3num3 2; 29 % checking whether absolute difference is less than 0.001 30 % if yes then break from loop 31 if abs (pi - estimated_pi) < allowed_err 32 break 33 end 34 end

Command Window Estimated pi using Nilkantha Series: 3.140881 Iterations conpleted: 7