Question

7. Use your class to calculate rational approximations for π using the series π=1-1+1-1+, . Your program should ask the user how many terms to include in the approximation. For full credit, use the class above as much as possible (to do all the calculations)

Answer 1

Given series

$\pi =\frac{4}{1}-\frac{4}{3}+\frac{4}{5}-\frac{4}{7}+......$

above series can be written as

where n is the number of terms included

2i-1

Matlab Code:

clear variables
close all
clc
n=input('\n Number of terms to be included for approximation:');
pi=0;
for i=1:n
pi=pi+(((-1)^(i+1))*(4/(2*i-1)));
end
fprintf('\n Approximate value of pi when %d terms are included is : %f\n',n,pi);

Sample Output: